Virgin Media bought out Telewest, so should be pretty widespread. But a word of warning before you sign up. The service is pretty good. We have a 30mb line (which they are supposedly upping for free) with unlimited bandwidth, so they say - we don't do large downloads so haven't been throttled - but it can be brutally slow and sometimes just drop out from seconds to hours. If you are working from home, that could be an issue. That being said, no internet line is perfect so just compare the costs.
The warning is about their contracts. They will make you sign a year contract, and if for any reason you need to get out of it, they will charge you a huge fee. No exceptions, even if you are moving house. So my tip is to really do your research on cancellation policies of the companies you compare!
When you are looking around the flats with the estate agents, look for ethernet type outlets (these will generally be phone lines) and coaxial cable/aerial outlets. Also look for Telewest Broadband written on the outlet; that could mean that previous tenants/landlords had the place wired for cable, and that is now Virgin Media. Rule of thumb is that the newer the property, the more likely the place is wired up with something. Oh, and it goes without saying, if the place you decide you like is not wired up with the connectivity you need - put that in your offer to rent!