Does anyone know what London would be like at the end of June? Not sure if things will be too crazy there the month before the Olympics begin, Is it better to avoid London at this time?

London is a big city and all the Olympics stuff is happening in the East End. The main tourist sites might actually be a bit less crowded,
It might even be easier to get into theatres and decent restaurants.

London is a huge city and the Olympics dont start until end of July...end of June will be busy for tourists, but not any different than any other year I would imagine.

Why would London be "crazy" a month before the Olympics?

The bits visitors go to are almost completely insulated from the games, and the Diamond Jubilee (which will attract far bigger crowds, and into the centre as well) will be well over.

As Miss Prism says, the likelihood is that tourism will decline anyway, so if anything the tourist bits will be emptier. Few tourists ever bother with decent theatres and restaurants, so they'll be as full as ever (the real business of London is utterly unaffected by a sporting event) - but the "Wicked" and "Les Mis" kind of theatre will probably be easier than usual to get tickets for.

There'll be a bit of Olympic preparation-linked traffic disorder round The Mall and its approaches, and the serious construction work in the centre, unconnected with the Olympics, will be ongoing till 2016. But some traffic disruption's pretty standard all year round anyway.

Define "crazy." London is the largest city in Western Europe, by far, and its size alone may lead you to think it's "crazy" at any time. It is almost always packed with tourists. Just deal with it.