The fastest way is going from King's Cross St Pancras tube station to Paddington tube station first via Hammersmith & City line or Circle line/Circle line and then interchange to the Heathrow Express at Paddington rail station. The trip takes about 30-35mins, plus 5-10 mins from the rail station to terminal 2 and <20mins waiting time (<5mins for tube and <15 mins for heathrow express). The trip costs £24.5.
On the other hand, since you have enough time, I would recommend Michael Hampton's answer. The trip takes half an hour longer but costs only £6 and waits 10mins less.