In 1827 John Baxter married Ann Richards at St Neots, which fits with the census family that John found. Baptisms at St Neots of children of John and Ann were:
Benjamin 13 Sept 1829
John 13 Sept 1829 (privately on 2 Sept 1829)
William 31 Jan 1831
John is described as a labourer each time
Harriett Florence Baxter was baptised on 6 April 1856 at St Pancras (born 28 Aug 1838) dau of John and Ann, clerk, of St Stephen's Terrace. She may have decided herself to add her middle name, Florence, as 1856 would have been at the height of Florence Nightingale's popular fame.
I wonder of Harriett exaggerated her father's status - she wouldn't have been the first to have done this. He seems to have had career changes though, labourer - clerk - engineer!
It will be interesting to see if on Benjamin's marriage cert his father is described as John Oliver, or just plain John. I can't see a marriage in Hunts between a Baxter and an Oliver, nor can I see a baptism of a John Oliver Baxter in St Neots
Have you found Ann in 1861 and 1871? What are the references as I'm struggling? Virtually no sleep last night on the train may be a factor!
But "former laundress" in 1881 ties in with "laundress" in 1851
John - have you got the NBI to see if there are any John Baxter burials 1837-41 in St Neots? I've sent mine off to get the upgrade to NBI3
David