I did notice quite a queue for the economy check-in at LHR when I once travelled early in the morining - and you need to be at the check-in desk 30 minutes before departure (i.e. not at the back of the queue). If you are in business or *G then I would arrive no later than 45 minutes before the flight, but in economy (without status) 1 hour is fine.

If you do arrive earlier (and to be honest somebody has to - the 30 minute check-in deadline doesn't work if everyone turns up then), there are lots of shops to look at in the terminal, and you can get a coffee etc.