Have not found a Francis Beechey but i found Ann Collicutt baptised in Ebrignton which is not all that far from Bourton on the Hill. Seems all their children were baptised at Bourton on the Hill.

parents: Underhill Collicut,​ Anne

name: Anne Collicut
gender: Female
baptism/christening date: 24 Nov 1745
baptism/christening place: EBRINGTON,GLOUCESTER,ENGLAND
father's name: Underhill Collicut
mother's name: Anne
indexing project (batch) number: C02806-2
system origin: England-ODM
source film number: 857053