When you see a date reference in the form Q4 1968, you are looking at what is referred to as a quarter date.
In the United Kingdom, once births are registered, a summary of the information is collected and published in a quarterly index. You can use the index reference to order a certificate for England and Wales via gov.uk -- the same page has links to separate pages for Scotland and Northern Ireland.
HM Passport Office's Guide to Birth Certificates outlines how the system works, and has illustrations of what the index pages look like, as well as a sample certificate. (Similar guides exist for marriage and death certificates.)
To illustrate how the system works, I'll use a search result from the site FreeBMD, a non-profit site whose goal is to make the indices available to the public. I looked for entries for Harriet Rossiter, one of the names from my own research, and here's one of the results:
Births Mar 1898 (>99%)
Rossiter Harriet Taunton 5c 299
Mar 1898 refers to the first quarter. On other sites you may see this written as Jan 1898 or Feb 1898. My personal preference is to write Q1, which makes it obvious the date is a quarter date reference, rather than an actual month.
Taunton refers to the Taunton Registration District. You may see people pencilling this in as the birthplace, and to remove ambiguity, my preference is to write out "Taunton Registration District". (I'm a bit of an extremist because I've created custom birth, marriage, and death registration events in my software to store this information, so I won't fill in the place of birth with the town the registration district is named after, and then send myself off on a wild-goose chase later.)
5c 299 refers to the volume and page of the index where the entry was found. A full reference has all four of these elements -- quarter date, registration district, volume, and page. The notation
(99%) is FreeBMD's way of telling you how much of the index for that particular time and place has been indexed.
More modern entries may have more information, such as the mother's maiden name.
Predicting Birth Dates from the Registration Date
The following quote is taken from a different guide to birth certificates, also from Gov.UK, which was written for people who might have to tell whether a certificate has been forged or not.
When a birth occurs in England and Wales there is a legal requirement
for it to be registered within 42 days, although it is possible for
births to be registered after this time. The registration is made by
a registrar (or deputy) in the registration district/sub-district in
which the birth occurred. Once registered, certificates can be issued
from the entry either centrally at the General Register Office (GRO)
or from the register office for the district where the birth occurred.
There is no restriction on who can apply for a birth certificate,
provided the birth entry can be identified.
This means that for someone whose birth was registered in Q4 1968, they might actually have been born at the end of Q3 (i.e. in September), usually within that 42 day window, but their birth wasn't registered until the start of Q4 (i.e. in October). It's possible that some birth dates were mis-reported so it would appear the registration was made on time (to avoid fines for making a late registration).
Predicting Birth Places from the Registration Place
If you have the registration district and want to see what places are included in the district, here are some useful sites to look for that information:
This policy document has additional information including how to order certificates for unusual cases such as people who were born overseas, and some restrictions about who can order certificates.
Formatting of Dates
For precise birth dates, dates in the UK follow the convention dd mm yyyy instead of the US style of mm dd yyyy -- for clarity, it is better to write out the month so it is clear to everyone what date is meant. It's better to write (as you did) "12 August 1931" because when written in numbers only it would be 12/08/1931 in the UK and 08/12/1931 in the US, which would be read as a different date by researchers on different sides of the Atlantic.
Have You Found the Right Person?
In the case of the linked Wikipedia article, the article author may be using quarter dates as a privacy shield. But whenever you see a quarter date, that may be a sign that the person using that date has not seen the certificates -- and it may mean that the reference being cited doesn't belong to the person being written about, but instead refers to someone else who has the same name.