Thank you very much for all the information. I have Jane as born in Benson abt 1803 (from 1851 census,) so the Thomas and Ann Hedges marriage looks like the right one.
The baptism for Benjamin in Woodstock does seem a little early, his age in 1841 would make earliest year of birth as 1806 which ties in with age at death. The burial information confirms the registration in Woodstock district was his after all. Strange that Jane (now confirmed as a widow) did not marry John Eltham. I have now found that the child Emily Eltham (with John and Jane in 1851) was called Emily Churchill in 1861 when Jane was living seperately from John and caling herself a Churchill again. John is a lodger with his married daughter Elizabeth Adelaide and her husband Edward Franklin(g). So still not clear whether John was Emily's father, but now confirmed, definitely not Benjamins. Emily's pob is given as Hensington the same as Richard and Mary Churchill and not Eynsham as might have been expected if she was John's child.
There is a Benjamin Churchill in 1851 who was born abt 1803 in Woodstock (widowed farmer living in Tackley) who is a better (but not perfect) fit with the 1801 baptism. A previous reply mentions baptisms in Deddington and there is a Benjamin in 1806, but Deddington is quite some distance from Bladon (at least for those days), although there must have been a lot of people travelling some distance from their original homes to work on an estate as large as Blenheim.
So as my Benjamin was a carpenter he could just pack his tools and move where the work was, so Deddington is still a possibility, unless the Deddington Benjamin is definitely dead before 1843 or definitely alive later than then.
I still feel the name Claydon is significant somewhere and to name two sons Richard might mean we're looking for a father called Richard.