If there's no bus from the gate to the T1/2 Connection Centre, and you don't mind clearing UK immig./customs, then I concur on the Heathrow Express Train advice. (Warning if lots of luggage: trolleys not allowed on the platform.)

Otherwise, you'll have to walk through T4, following the "Connections" signs, get on the regular bus to the Connection Centre, etc. One hour, 50 mins. should be OK if there are no inordinate delays, but not by a lot!