Palmer of Cold Brayfield?

[Taylor94]

Im trying to find the parents to my 5th Great Grandmother Mary Ann Palmer.
She marries Thomas Johnson 7 April 1821 St Margarets, Leicester, Leicestershire. Both are listed of the Parish and Mary Ann is a Spinster, She does not sign but leaves a mark.

On the 1841 census, her birth date is given as 1806 and she is listed as born in Leicestershire.
On the 1851 to 1871 censuses her birth date is given as 1803 and her birthplace as 'Cold Brayfield, Buckinghamshire'

I thought I found her baptism as 'Mary Ann Palmer, daughter of Thomas and Mary Palmer, 6 Jun 1802 Cold Brayfield, Buckinghamshire' But then I can see a burial for the same Mary Ann Palmer on the same date according to FindMyPast.
I cant see any other baptisms fitting?

The only one which I can see is a baptism in 1801 for a Mary Palmer in St Margarets, Leicester. Daughter of John Palmer and Fanny. This goes against what she has wrote on census as her birthplace though.

Any help appreciated.

[Taylor94]

A John Palmer and Fanny Wadsworth marry in Olney, Buckinghamshire in 1798. (Olney is right next to Cold Brayfield)
They then seem to move to Leicester and then baptise a Mary in 1801 St Margarets.

This theory seems to fit although there is a marriage between a John Palmer and Fanny Freer 1795 St Margarets.

[Taylor94]

A John Palmer, Yeoman, of St Margarets has a probate granted 1840 and mentions wife Fanny and daughter Mary Palmer, Spinster.
I think this must be the Mary who was bapt 1801 St Margarets to John and Fanny.

So back to square one now.