Hi Pat
I'm nearly out of brilliant ideas on this one I'm afraid.
There were no birth certs pre 1837 so the best you can get is a copy of his baptism entry in a parish register.
That assumes that he was baptised (not everyone was) and even if he was, where?
In the two censuses in which he appears he gave his birth county as Hunts in the first and Cambs in the other. All of Cambs parish register baptisms have been transcribed onto the 1801-37 index on by Cambs FHS and he's not there.
Hunts is a different proposition as there is no central index as there is for Cambs for the likely period of his birth, and many parishes do not appear on the IGI, as the LDS was refused permission to film the registers. So for many parishes the only place to view them is at Huntingdon, which if you live in the USA or France makes life a bit difficult.
I have a feeling that he may have been born in Hunts, but it's a bit like looking for a needle in a haystack.
You can safely ignore the IGI entry of 1816 at Old Weston. The LDS church member who submitted it didn't have a clue when or where he was born so deducted 25 (it being assumed that males married at 25) from the marriage year, with the place being the same as the marriage. Pure worthless fiction!
As you know that Harriet had a legitimate father it's possible that the fathers' names were simply missed from the marriage cert, and William wasn't illegitimate at all. Alternatively, because he WAS illegitimate and didn't have a father's name to provide, Harriet left hers blank as well. Could be either.
In 1841 the head of the household was George Taylor, but one of the others in the household, possibly his brother, was Abraham Taylor.
You could try checking the parish chest entries of Alconbury Weston to see if there is any trace of a settlement certificate which would give his home parish.
I've had a look at the A2A index on
http://www.a2a.org.uk/search/index.aspand found the following
http://www.a2a.org.uk/search/documentxsl.asp?com=1&i=12&nbKey=2&stylesheet=xsl\A2A_com.xsl&keyword=gray&properties=0601QUARTER SESSIONS BOXED PAPERS - ref. HCP/1/40 - date: 1857
March, 1857 Hunts. Assizes: Harriet Gray 34, widow Able to read; Leaving infant child without food or covering at Buckden. Sentence deferred
This looks very much like your Harriet. You could try contacting Huntingdon Records Office to get more details, which might shed some light on William - perhaps sentence was deferred pending reports from social services. Or is that a 20th century phenomenon?
Best I can come up with I'm afraid
Good luck
Regards
David
PS Just had the most obvious thought. Could he have been baptised in Alconbury Weston? There are a lot of Gray burials there at about the time he would have been born. Post a specific look up request on the Hunt look up board for his baptism - the parish records have been transcribed by Hunts FHS are on fiche (and Ruth has already checked them on this thread!)