ottages yes, but churches? There’s about a hundred of them, half of those in Norfolk (see Michael Billett’s English Thatched Churches).
Markby is the only one in Lincolnshire, built c.1540 using stone from the ruined Markby Priory. It was tiled until 1672, when a churchwarden swapped the tiles for thatch, and last rethatched in 2008. Norfolk’s Barton Bendish St Mary has been unlucky and lucky. Its tower fell in the 18th c. and was never replaced, but later it gained a splendid Norman west doorway from the demolished All Saints church.
A little further south, by the busy A134 (and hard to spot among the trees), Cranwich sits in a circular churchyard the sign of an early site. Its round tower has Saxon interlacing sculpture in it belfry windows. Just over the border into Suffolk, at ‘Ihornham Parva, even the little late 15th c. tower is thatched. Insid is the wonderful early 14th c. Thornham retable, probably made for the Priory a Thetford; the other half is in the Muse de Cluny in Paris.
In SE Norfolk, there’s Hales, the beau ideal of an East Anglian Romanesqu church, hardly altered since its building