I have no experence with huge demands, but i am sure the people over at www.ukwsd.co.uk would be able to handle it. I have hosted about 6 different sites with them over the years and they are awesome.
I have reccommended a company in the States that does alot of hosting for UK based companies to my clients. I have never had any problems with them and they have great support 24/7. The company is www.neospire.net. You can fill out a form on there site and someone will call you back.
I was going to recommend fasthosts, I've not had any trouble with them... except for one day this week. But by the time I found out, and had a word with my colleague, the server was up again. I suspect it might have something to do with the weather.
Customer suport was nice and speedy whenever I've had questions.