There are so many good hosts, it is hard to pick just one.
But you need to be suspicious to those who claim they can offer real bargain service and get everything you want.
Asking for unlimited anything is not reasonable. Specify want you want an shop prudently. Now take a look at this:
http://www.1and1affiliate.com/tips/press-affiliate-news/unlimited-traffic/Do y0u think they could really, really offer unlimited anything? Even with fiber optics, the servers themselves have finite number of CPUs and a finite bus bandwidth inside the box. And if one has unlimited bandwidth, then why do some customers pay three and fours times as much as what the OP stated, 15 ponds.
Dedicated servers lease for about $150 per month, more or less. It gives as much bandwidth as nit can. These people want to talk to you first, then tell you want you need:
http://www.rackspace.com/hosting_solutions/ But don't let them talk you into want you do not need.
In the UK, check out
http://34sp.com for competitive prices.
And no, I am not part of any of them. Just trying to be helpful.
Forgot to mention:
http://netobjects.com/For some, it could be a good choice.