Searching for English and Welsh BMDs the first source you consult should be the Civil Registration indices which were kept for all birth marriage and death events from September 1837 onwards. Theoretically, these should be complete (in practice, they're not -- there are omissions and indexing errors, but they're still your best starting point and you can access them free at freebmd.org.uk The indices are organised by year, quarter and registration district -- excellent instructions for searching are here.
You will find evidence that a DANIEL DENEHY married one of MARY HARNOTT or ELLEN O'CONNORS in Q2 of 1883 in Monmouthshire, Wales. To get more detail, including verifying that this Daniel married Ellen and not Mary, you would need to order the certificate from the General Register Office quoting the reference details you have obtained from FreeBMD (Year, Quarter, District, Volume and page). However, a marriage in 1883 puts Ellen's supposed birthdate of 1872 out of the question -- one or the other is wrong. (There's also a potential mismatch between her birthdate and her son's -- 16 years old is unusually young to be having a child in Wales at that time).
Thomas's birth may be harder to track down as his forename isn't uncommon, and neither are the variants of his surname, and there might be too many certificates that are possibles to be economic to order but FreeBMD would be your starting point again.
The other major source for England and Wales in this period are the censuses taken from 1841 every 10 years. FamilySearch.org has indices for these but you will have to use a subscription site to see the images and full details in most cases. You should be looking for Ellen before her marriage in 1881 and possibly 1871, and for the family in 1891 (assuming they didn't emigrate before then).