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Who seems to be him was buried at Kempston on 22 Jan 1852 age 87. In 1851 he was living in nearby Wootton age 86 born Kempston. In 1841 he was living in Kempston age 75.
So his birth seems to have been c1765 in Kempston.
There are no banns in the Kempston transcript so presumably he was resident in Cranfield at the time of the marriage
But as you say, there are no suitable baptisms in Kempston around that date, and only two in Beds within 5 years of 1765 and they were at Gt Barford and Biggleswade, neither of which are particularly close to Kempston. There are no Johns baptised in Kempston in 1765 +/-5 with a surname that could be a corruption of Lambert. But there was only one Lambert couple baptising children in Kempston 1765+/-10 - Thomas and Isobel. And one of the children, Elizabeth, was baptised 5 years late. Perhaps they forgot to do John altogether. But John and Jane didn't name any of their children Thomas or Isobel.
There's a burial of Thomas Lambert age 85 on 21 Feb 1822. Your only hope is that he left a will, naming his children.
You may be in luck.
BLARS has a will of Thomas Lambert senior of Kempston, carpenter ref 1822/10. Pity you didn't post your message before you spent a week at BLARS, as it will now cost you a few quid, not many, to get a copy of it. I think their minimum charge is a fiver, so you might want to get the will of Thomas Lambert of Kempston, victualler ref 1834/9 as well. He was buried age 66 at Kempston on 11 Nov 1833, and could have been a brother of John. He might name a brother John in his will.
Jane Lambert was buried at Kempston on 28 Nov 1813 (no age given) and Isobel Lambert on 29 Sept 1803 (no age or other detail)
David
I hope to be spending a week in Bedford in July visiting the archives and my aged mother, and many local hostelries - I live in the south of France!