The first thing you should know is that it's now EU law that a UK provider has to give you data all throughout Europe at no extra cost (winning!). So don't worry about finding a provider that you can use on your travels, because they're all now pretty much the same in that respect.
The following providers currently offer unlimited data plans:
But in fairness, most other providers offer relatively large data plans as well.
If you've got proof of address already when you move to the UK (because you've used a mate's address or something) then you can just walk into a store and grab a SIM card on day one. If not, you may have to wait. Again, that's constantly changing and does depend on the individual provider, so it can't hurt to do a quick Google search before you start walking the streets.
Other than that, most providers give you unlimited talk and text as standard and coverage is generally solid throughout London for all of them.
The following providers also give you FREE WIFI on the tube (at tube stations):
You can use a site like money supermarket to do a quick cost comparison and work out which is best for you.