Hi,
Not knowing London at all could I suggest two important principles. First for the meet you want to be safe. That means no one carries weapons, so somewhere weapons can't be brought - think airport lounges where they hopefully have metal detectors. It also means that you don't want even busy places where a sniper could be sitting in a building overlooking the meet. And just as an extra, you want it to be a place where everything is on video. That way if something does happen, the police know who to hunt - which acts as a deterrent.
You also want to be able to arrive and leave without being followed, so the underground works well for that.
So my best guess would be something like an important museum or art gallery where there areguards, cameras and metal detectors, plus no good sniper possies. And hopefully multiple entrances. It would help if your MC knows people who can gain him access to the back way out.
Cheers, Greg.