Goodness me there is no need to do that. 
It was possible it was an error by the Vicar if he made the entry at a later date
on the baptism entry.
I think the fact neither could write means William could have been the plasters labourer
who went with his family to Lambeth being there in 1861?.
If you would like me to look at the originals Brackley P.R.'s for you if you could give me
some dates it might help to link the families.
I believe baptism and burial registers were made up later rather than at the time. I've certainly seen registers where the mother's name is missing but is present in previous and subsequent baptisms.
Yes, I think William did end up in London. The Lambeth family is a pretty close match for the Brackley one.
The only information I am now certain of is that Thomas was baptised 2 Mar 1777, son of Christopher and Ann (nee GARDINER) in Finmere, Oxon. There's nothing in the notes I have that give the marriage of Thomas to a Mary. There's apparently a removal order for Thomas and Mary back to Brackley St Peter from another Brackley parish. I don't think that would have happened if he was a glover but is more likely if he was a labourer of some sort.
Thank you for your kind offer but please don't worry. It seems unlikely the Brackley family is anything to do with my own line. Thank you also for pointing out my error.