Hmm, just found the will of Thomas Atkinson Esquire of Dean Street, Saint Ann Soho, Westminster, Middlesex, written in 1803 and proved 1807, but his wife is Elizabeth and I can't see any mention of children on a very quick look through as I am supposed to start cooking the dinner about now:
PCC will on ancestry
He must be the freeholder listed in the Poll Book but perhaps not your Thomas.