One last thing, do you think these Woodhams could have been 'dissenters' ie Baptists or some such, and that's why they wouldn't be in parish records which were the records of the 'established' church?
Yes, I think it is highly likely they were Baptists. One reason I have for thinking this is that I found the following births on FamilySearch:
26 Feb 1809 Gabriel WOODHAM, son of William WOODHAM
26 Feb 1809 William WOODHAM, son of William WOODHAM
Both were recorded at Old Meeting House Baptist and Independent, St Neots, Huntingdon. It looks like they were twins and, because of this, they may not have survived to adulthood. The reason they caught my eye is the use of the name Gabriel which was also used by George WOODHAM the son of the William born circa 1786.
Incidentally, although the William born circa 1786 is listed as being born in Scotland in the 1841 census this is incorrect. I believe that the tick placed in the column indicating that an individual was born in Scotland, Ireland or Foreign Parts was just a mark made by the enumerator when he was checking those not born in the county. If an individual was born in Scotland it was usual to put an 'S' in this column. Likewise if an individual was born in Ireland there would be an 'I' in the column and an 'F' for those born in Foreign Parts.
With regard to records kept by Baptist churches the short answer is that these varied. Most Baptists only baptised adults and records of these are most likely to be found in the Church Minute Books. Some churches, such as that mentioned above, kept records of births, and some kept records of deaths and burials too. However, prior to 1837 all nonconformists other than Quakers and Jews had to marry in the Church of England so there should be a marriage for William and Sarah WOODHAM somewhere.