Departing LHR and when able to use the First or Business checkin line (by ticket or by status) and without the ability to use the Fast Track security line, 2 hours from arriving at the airport is plenty enough and even gives me a decent time for a breakfast in a lounge (BA Galleries for preference, of course). I start to hurry when it looks like arriving less than T-90 mins because the LHR cutoff of checkin 60 mins before flight is strict and there may be a queue or random other problems.
I would only arrive 3 hours before if I really had some time to spare or had something interesting to do, for example if I had access to all the Oneworld F lounges and wanted to do some lounge-tourism.