Sorry, I didn't know they had gone to India!

Anyway, all I did was a free search on the 1861 census via Findmypast.com, with a dob of 1840 give or take 4 years, and lo and behold one of the many Charles Bradley's was residing in Burton Upon Trent, and his dob (1843) wasn't too far away from 1840...

Worth a try!