Well, I suppose its not beyond the realms of possibility that a labourer could become a baker in later life, but it doesn't really seal the deal, does it?
I notice that by 1837 when Thomas's youngest sibling Jane was baptised, John (the father) is described as a husbandman, so he's either gone up in the world a bit or likes to think he has!!

I seem to remember reading somewhere along the line ( can't remember where!) that some small farmers would mill their own flour and bake their own bread, so it's possible!
It's a pity that Jane was born just before civil registration was introduced, or you could have sent for her birth cert.
I think - if you haven't already - you need to see if you can find John & Ann - and Thomas - on the 1841 & 1851 censuses. There's a good chance they might both be still alive.
I'll take another look at the Horspath PRs and see if I can find burial dates for John & Ann and then, if they died after Sep 1837 you could perhaps send for their death certs.
I'll get back to you.
Jill