OP could in fact consider East Anglia as a destination, maybe basing himself in Norwich and making day trips to Cambridge, Ely and into the Broads. I wouldn't say it was very convenient for LHR though.

I don't think Cornwall is deficient in historic sites there are castles, stone circles, churches, lots of historic houses of all ages/sizes and masses of museums. Admittedly there is a lack of large and grand buildings and it won't appeal unless the OP is interested in maritime, agricultural and industrial history.