There are a wide variety of internet service providers from whom you can buy dedicated hosting services. The key thing is whether they will either have software installed already, install it for you, or give you a virtual machine to control completely.
Most of the larger ISPs will rent you a dedicated server on a monthly or yearly basis, as will Domain Name registers. A random selection of UK options include BT, Easyspace, and Fido.
Amazon offer Elastic Cloud Computing where you can essentially get hold of either a real or virtual computer of various specs, with adminsitrative control. Although there is a charging model you want to keep a strong eye on, for web servers there are options which are free with certain data/hit limits for 12 months. After that, there are various purchasing options with various prices. For more information about setting up in the cloud, see their Getting Started guide. Google have a similar Cloud Platform.