First of all, the UK is very close to the core network centers of Europe, so hosting in Amsterdam or Duesseldorf should provide sufficiently low latency for anything except stock trading applications. I mention this because a lot of hosting companies selling in the UK market, make it very hard to figure out where their servers are actually located. But for most people it doesn't matter since Europe is a lot more compact than the USA, with very good connectivity internally. Location really does not matter.
Amazon EC2 is available in Europe and they are the leaders in allowing new machines to be turned up quickly and effortlessly.
There are probably now dozens of hosting providers in the UK providing XEN-based virtual servers. Not sure about the USA, but here in the UK the common terminology for this is VPS hosting so if you go to http://www.google.co.uk (not .com, this is important) and check the "pages from the UK" radio button when you do your search, you will come up with numerous possibilities in both the results and the ads.
And some like xenEurope do advertise their automated 24 hour provisioning so what you want to do is possible.
