There's really at least two different events happening at the same time, sharing a hotel. One is a conference with panels, speakers and quiz games. The other is the annual reunion of the people that go to Eastercons. I generally go to see one or two programme items each day, the rest of the time I'm either in the bar or wandering around whichever town we find ourselves in. The latter is not really viable at Heathrow, there's bugger all to do in the immediate vicinity of the hotel. As someone has already pointed out, there are a lot of cliques at the Eastercon, people that have known each other for years. What isn't immediately obvious is that the cliques aren't closed and will usually accept anyone who happens to wander by. If there's an interesting conversation going on (invariably in the bar) then feel free to join in. Members wear name badges so that they can address complete strangers by name.
There are some areas where there is continuous programming on one topic. There are some people who go to the con and spend most of their time making costumes for the masquerade. There are others who spend all of their time playing role-playing or board games, including most of the night. Incidentally, the convention doesn't shut down when the programme ends. There are usually a few organised parties supporting future convention bids and some more smaller ones running in hotel rooms. They go on until the small hours though there are usually a few people still wandering around when the hotel opens for breakfast.
If you are the type of person who finds it difficult to introduce yourself to complete strangers then consider volunteering to help out. Warning: this can get addictive. I've been known to fly across the Atlantic to work on a convention. It's a good way to get to know people quickly.