I flew out last month from Terminal 3. It took me roughly about half an hour to get through security. This involves the usual x-ray of your carry-on, and a walk through passport control, (only ever glance at my passport, if there is even anyone there) and then you have to pass your footwear through x-ray after that. However, when I have traveled at peak periods, (which I think now might qualify since it is summer) it has sometimes taken me almost an hour to get through security.
I think the longest time can be just checking in at the airline. I always travel American (airmiles!) so I can only speak to that experience, and I don't know what the other airlines are doing. They have recently opened up a DIY check-in and that has cut down the waiting time considerably. That line used to be hideously long.
American has a new gate area that it is flying out of, and it takes a good 10-15 minutes to get there from the waiting area. As others have mentioned, there are plenty of places to get a cup of coffee or other beverage once you get past security. There is a huge duty free department, as well as high street shops like Boots, WH Smith, HMV, Curry's and high-end retailers like Harrod's and Burberry, so if you get there early, and sail right through security, you needn't be bored just sitting there!