This isn't a complete answer, of course - you are probably right that DNA testing would be required for that. But I hope this can help frame further research into the family/families at the centre of this. I'm going to look at the will, a baptism record, and a few of the named people. (And my apologies, this turned from a comment into an essay, and then got rewritten late on when I found more sources!)
Let's start with the Will. That is in Ancestry's "England & Wales, Prerogative Court of Canterbury Wills, 1384-1858" database for "John Stanford Gerdler". I'm not going to transcribe the whole thing, but I recommend you do, if you haven't already, and pick it apart so you know exactly who was mentioned, and what they received or were responsible for. (If the transcription is tricky in places, ask another question here and someone will help!)
The will is dated 23 Jun 1820 and was proved in London on 30 Sep 1820, so it was written shortly before John's death, and therefore is "up to date" in terms of people's names and such.
My reading of the will is as follows.
John leaves his estate to "Mrs Mary Hickman" and "Thomas Henry Stirling Esq", and their respective heirs, as "Executors and Admons" (I think). Mary and Thomas are thus given control of the estate so that they can manage the investments and annuities.
The will includes a critical passage:
"a yearly payment of one hundred pounds to be paid by [Mary and Thomas] for the maintenance and education of James Stanford Scott an Infant of the age of five years now resident with Mrs Mary Hickman at No 13 Alpha Cottages until he attain the age of twenty one years who I recommend to be brought up to the profession of the Law if agreeable to him and approved of by my said trustees whom I desire to act as his Guardians"
This is valuable - it names James Stanford Scott, and gives his address, and tells us that he was living with Mary at the time. Later in the will, property is left in trust for Mary for the term of her life, and then in trust for James after her death, but would revert to Mary if James died before the age of 21.
So James Stanford Scott is the principal beneficiary of John's will, and Mary is also a major beneficiary. Both are clearly important to John, although no relationship between them and him or each other is given. The will names no family members at all, in fact. Meanwhile, Thomas is described as John's friend, and John's godson, John Stanford Smith, is also mentioned, along with several other people of no stated relationship. That Stanford name seems significant, so perhaps try to identify the godson's parents to see how they relate to John.
The will was proved "with a codicil", but the codicil is not included in the Ancestry record. It may be worth trying to track down, as there may be some useful information in there. Additionally, note that John's will was witnessed by J. Hickman - a coincidence, or was he related to Mary Hickman?
I think it's interesting that James is living with Mary at the time of the will, and that she and Thomas are requested to act as James' guardians. In a comment to another answer, @Ladyslug said:
In the 1851 Census he is widow living with his mother… Mary Robinson who is Mary Hickman from the will
I can find that census entry (HO107, Piece 1573, Folio 775, Page 31). It does say that Mary is James' mother (not guardian). An Old Bailey record of James' 1877 trial for perjury also gives "F. Mary Robinson" as James' mother, and it refers to transfers of the annuities and properties mentioned in John's will. That warrants further study, and also trying to find the original Scott vs Wood trial details.
A newspaper report on that trial, in the Leicester Daily Mercury on 20 Feb 1877 (findmypast link, also on the BNA etc) is quite enlightening:
The plaintiff, James Stanford Scott, was the illegitimate son of one Mary Hickman, who afterwards married a Mr. Frederick Robinson. Mr John Stanford Girdler, late of Brook-green House, Hammersmith, who died in 1820, by his will made shortly before his death, after making provision to the extent of £100 a year for the plaintiff, gave his residuary real estate to trustees upon trust for Mary Hickman for life, with the remainder to James Stanford Scott, the plaintiff, in fee.
The report clarifies that properties from the will were sold by Scott, in 1846, but he attempted to recover them in court nearly 20 years later, claiming that the documents of sale were forged. The perjury trial arose from his apparent dishonesty in that action.
The question states that:
On his christening it lists parents as Mary Scott and John Stanford.
What is the source of this claim? Is this a typo, or is there a record that actually says this? Because in Ancestry's "London, England, Church of England Births and Baptisms, 1813-1906" database, I find an entry for James Stanford Scott on 08 Aug 1819:
This baptism record has James Stanford Scott, son of Thomas (a Mariner) and Mary Scott of 13 Alpha Cottages, Mary Le Bone. The baptism is in 1819, around three years after James was supposedly born, but that's not a particularly unusual thing. This record does not agree with the claim in the question that the father's name was John Stanford, which is more of a problem. The address here, 13 Alpha Cottages, matches the address of Mary Hickman (and James) in John's will. That seems an unlikely coincidence - this is surely the correct baptism. (So my comments on the question regarding the Stanford/Scott naming are no longer relevant.)
When the will was written, just 10 months later, James was still at 13 Alpha Cottages, but with Mary Hickman. There seem to be a few possible explanations:
- Thomas Scott died and Mary Scott remarried a Mr Hickman in the intervening 10 months. There's no obvious record of this, and in Mary Hickman's marriage to Frederick Robinson she is a spinster, not a widow.
- Thomas and Mary Scott both died, and Mary Hickman moved in to care for James. Mary Hickman is repeatedly described as the mother of James, so this doesn't work.
- Thomas and Mary Scott are not correctly named, and James was already living with Mary Hickman, his mother. This seems to me the most plausible answer.
There are questions, still. If Mary Hickman is James' mother, why is she not described as such in the will, and why is she asked to be his guardian? Perhaps this was John's way of "legitimising" the relationship, giving Mary lawful care over her own illegitimate son. And who was "Thomas Scott"? It could have been John Stanford Girdler or, perhaps, his friend Thomas Stirling stepping in?
John Stanford Girdler
A Google search for "John Stanford Girdler" doesn't bring up too many results, and it starts to look like a unique name. That's always a dangerous thing! :)
John seems to have come from a fairly wealthy and well-connected family. The snappily-titled "A Genealogical and Heraldic History of the Commoners of Great Britain and Ireland Enjoying Territorial Possessions Or High Official Rank, But Uninvested with Heritable Honours" has an entry for Sarah Wolferstan, daughter of Stanford Wolferstan (the likely origin of that middle name):
Sarah, m. in 1737 to Joseph Girdler, esq. barrister at law, son and heir of Serjeant Joseph Girdler, of Haselor, in the county of Stafford, and dying in 1781, left issue,
- Joseph-Bayntum-Girdler, who d. in 1787
- John-Stanford-Girdler, b. in 1751, of Haselor, m. Mrs Letitia Jones, and had issue
- Frances-Lucy Girdler, d. in 1801.
In "A survey of Staffordshire, with a description of Beeston-castle in Cheshire. To which are added some Observations upon the possessors of monastery-lands in Staffordshire, by sir S. Degge." we find a reference to Haselour, or Hasleover, passing through various families' hands until Samuel Dilkes sold it to:
Joseph Girdler, serjeant-at-law, whose great grandson, John Stanford Girdler, esq. now (1820) enjoys it.
The later "A Survey of Staffordshire: Containing the Antiquities of that County" reports that Haselour wa sold to:
Joseph Girdler, senior, sergeant-at-law, who died March 12, 1756 , and whose great-grandson John Stanford Girdler sold it, about 1822, to … Neville
Meanwhile, the "History, Gazetteer, and Directory of Staffordshire…" (the full title is around a mile long, clearly authors were paid by the title word) says that Haselour:
became the property of Joseph Girdler, sergeant-at-law, from whom it passed to two coheiresses; so that it is now in two moities, belonging to the Dowager Lady Chetwynd, and Thos. Nevill, Esq.
There are a couple of things to note here. The first of those references tells us that the John Stanford Girdler who married Letitia Jones was the grandson of Joseph Girdler, sergeant-at-law. The next two tell us that Joseph Girdler's great-grandson lived in and sold the property. That would mean that there were (at least) two John Stanford Girdlers alive at the same time, so we do need to be careful trying to separate them.
The last reference makes me think that the younger John might be the son of one of the elder John's sisters (i.e. the coheiresses), rather than being John's son. This might explain why John's will doesn't reference any children. However, the first link does say that John and Letitia had at least one child, so there may be more to find.
Ancestry's "London and Surrey, England, Marriage Bonds and Allegations, 1597-1921" dataset has an entry on 26 Nov 1793 for the marriage of John Girdler, "batchelor forty years" and Letitia Jones, widow, which matches the information above.
There is also a record in Ancestry's "Kent, England, Extracted Parish Records" set for the marriage of John Stanford Girdler Esq of Hammersmith, and Thomasine Mauleverer of Thanet on 25 Oct 1816. This could be John remarrying after Letitia's death, but I doubt it. John's will expresses his desire to be buried alongside his "much lamented and late wife at Hammersmith". We can find a record for a Letitia Girdler, buried in Hammersmith in 1811, aged 52, in Ancestry's "London, England, Church of England Baptisms, Marriages and Burials, 1538-1812" set. Thomasine doesn't appear to die until 1833, and John's will makes no mention of a surviving wife.
However, that Kent marriage does suggest that a younger John Stanford Girdler was living in Hammersmith at the same time as the elder John. It's not clear if they lived together or just in the same area, but that's another reason to take care in identification and attribution, anyway.
I haven't found any children for John and Letitia, even though one reference above claims they had issue. This is worth pursuing.
Thomas Henry Stirling
I haven't looked at Thomas in detail, and I think there may be some interesting things to learn about him. But there is a record on Ancestry in the "Cambridge University Alumni, 1261-1900" dataset for a Thomas Henry Stirling who studied Law at Magdalene College and was called to the bar in 1810. He was a senior "Puisne" judge in Ceylon (now Sri Lanka) and resided at Grove House, Battersea, where he died Feb 07 1864, aged 74.
This seems like a decent candidate for John's friend Thomas. There is an 1861 census record (RG9, Piece 370, Folio 115, Page 30) for a "Thomas Hy Stirling", Barrister at Law (not Practicing), at Grove House, Battersea, that matches the university record above.
There is nothing that I have presented above that directly supports or undermines the proposal that James was the son of John. That is still a possibility. It's also possible that John the younger was the father, and that John the elder was providing for the child to cover for his nephew/son. Or even, perhaps, that Thomas Stirling was the father, hence his position as co-guardian? That may be a stretch. In any case, we don't have any conclusive evidence either way.
What we do have is a claim (albeit unsourced, in a newspaper) that James was illegitimate, and thus that his parentage on the baptism record is false. Therefore John Stanford Girdler (senior) does appear to be a good candidate for the father. The Surrey Comet, 22 Aug 1903, reports briefly on the drunken behaviour of a "James John Stanford Girdler Scott", aged 51. That name alone suggests that someone else thought there was a strong connection between James Stanford Scott and John Stanford Girdler, way back around 1852!
I would say that full research into all of the relevant people here may still bring more information to light, and would allow you to trace the various lineages towards the present. And newspaper and court reports in particular might hold further clues about the money and relationships described above.
If you are able to trace living confirmed descendants of John Stanford Girdler, you may be able to try DNA testing, although the timescale means the results may have considerable uncertainty, unless you can identify unbroken male or female lineages for Y or Mt testing. (Don't take my word for it though. There are others here with far more knowledge than me regarding such things, and maybe one will chip in.) In the absence of that, having reviewed a number of sources above, I think your suspicions are quite well founded.