Hi Kim,
This might be a bit of a long shot, but there's a baptiism on the IGI at Stamford.
Although Stamford comes under Lincolnshire, it isn't too far from Peterborough - and it was a significant town at the time, where people very probably travelled to market, etc.
I've looked at other places near Peterborough, those that have records on the IGI, but can't see anything else.
Details are as follows:
Batch number: C031712 (Stamford St.Mary)
Sarah Johnson
Christening: 18 Sep 1796
Father: Wm Johnson
Mother: Lydia
Good luck with your search.
Paulene.