The only Garton in St Neots at around that time was baptised 2 Dec 1808 James son of John and Ann Garton, private Hunts Militia, born 29 Oct 1808. John appears to have married Ann Richerson in Eaton Socon on 8 Jun 1807.
There was a Jane Gardiner dau of William and Jane on 15 May 1806 but they also baptised Thomas on 17 Jun 1808 (born 29 Oct 1807)
1851 and 1861 give her birthplace as Eaton Socon Beds, but there's no likely Jane baptised there 1800-1810
But I see that the marriage shows her as Gardner, rather than Garton or Gartan. Do the birth certs of any of her children show her maiden name as Garton? If not where does the name Garton appear?
David