I think you have about three things mixed up into one thought there.
Domain Name Registration; Several options available in the UK, 123-reg, godaddy, ukreg to mention a few. Just Google Domain Name Registration and choose one based on your needs.
UK Domain Name Registrars; Once you choose a company to Register your domain that will be listed with Nominet, the UK Domain Name Registrars, Managing domain names on behalf of customers.
UK Web Hosting: A company that will provide Windows or Linux based web hosting solutions for you to load your website onto their servers.
For a web host, I would recommend a company called Storm Internet.