Hi Rob,
So, in the 1841 Census for Cowden, Kent.
Mercy BURFOOT (25) is in her father's household, and there is also a 1 month old Henry BURFOOT indicating he was born about May 1841.
HO107- Piece 481/ Book 7 / Folio 7 Page 6
I'm seeing his place of birth indicator on this 1841 Census looking like N (not Kent) to me!
Isn't his birth the one registered June Qtr 1841 in Sevenoaks? This is crucial to check - if it's Mercy BURFOOT's baby,she's then stating on census 1841 & 1851 that he wasn't born in Kent despite being registered there. If this is his birth, it may have some notation on the Cert about being physically born in another county (irregular, but not impossible).
And a year later in 1842, registered in Croydon Surrey is the marriage of William MAY to Mercy BURFOOT, dau of Christopher BURFOOT.
https://familysearch.org/ark:/61903/1:1:NVZ3-WJ4https://familysearch.org/ark:/61903/1:1:NJGT-WNH Subsequent Census show Mrs Mercy MAY was born in Cowden, Kent. I'm presuming there is little to no doubt she is the daughter of Christopher BURFOOT?
Checking that 1841 Birth would be more reliable, that trying to work out a year of birth based on ages (often 'out') given at marriage or Census. The most reliable ages for Henry are the 1841 and then the 1851.
Maybe Henry is William's natural child and for some reason William wasn't in a position (legal or otherwise) to marry Mercy before the birth, or for a year following it. However, for example, plenty of unmarried couples registered their children as legitimate with the father's surname. Or some were registered illegitimate in the mother's surname with the father's surname as middle name, later dropping the mother's name - lots of configurations and as many reasonings why!
Where I suggest to differ in your theory, is that William and Mercy necessarily had any sort of affair at all that resulted in Henry birth a year prior to their June 1842 marriage.
I'd say it would be much more likely that Henry's birth father is unknown (to us) and that when Mercy later married William, he simply took on the baby as his own and Henry became known thereafter as MAY. There is no law against taking up a name like this. And it was common.
Further it may be that Henry never knew he was illegitimate or that William mayn't have been his biological father. Maybe Henry was born (or made) in Brighton - but was registered in Kent, for whatever reason Mercy might have done that. Perhaps she was working in Sussex and removed back home to her Dad just after the birth.
If there is no suitable DEATH registration between 1841 and 1851 in any of the districts where Mercy lived during that time, for a son named Henry BURFOOT, that would further cement the probability that Henry MAY was the baby born Henry BURFOOT.
As to Henry's paternity, that may be something you can never fully clarify, bar DNA tests on suitable descendants.
Cheers
AMBLY