With such an unusual name, it's often helpful to plug it into Ancestry's global search.
I did that, and the 1841 shows just three Ingyons, a single family, all in Great Staughton, Hunts: Robert aged 60, a wheelwright; his wife (assumedly) Elizabeth aged 50, and Lawrence aged 15, all born in county. Lawrence is still there in 1891, also a wheelwright.
Successive census returns show the family spreading out into Northamptonshire - Kimbolton, Irthlingborough, etc - as well. But there are only ever 13 of them, if the name is typed exactly. There are doubtless umpteen variations and mistranscriptions - but hard to know which to use!
So I would lay a bet that Great Staughton and the surrounding parishes would be a good place to start looking for Jane. Not many miles from Potton, as the crow flies - about 12 miles, I would say.
Many of the Hunts parish records aren't available other than at the records office - and Great Staughton doesn't appear in Hugh Wallis's list of batch numbers for Huntingdon, so it may be one of the parishes that has never been filmed. But as I have just discovered, the records office does offer a research service at reasonable cost.
You can email them on
county.records.hunts@cambridgeshire.gov.ukHope this helps!
Wendy
PS A Google search just on the name brings up lots of fascinating info!