Welcome to FT ^. If you insist on using the tube...
According to my tube planner, take the tube from LHR T1 - Piccadilly line towards Cockfosters. Change at Hammersmith and take the Circle line towards Edgeware Road. It will take 57 mins and has one change.
I would not do it that way though. From LHR T1, I would take the Heathrow Connect to Paddington, and take the tube from there - 1 station hop taking 3 minutes (Connect is much cheaper than Heathrow Express). Or just take a taxi for the bit from Paddington as suggested above.