Companies like 1&1 click here will allow you to buy a Domain name. You don't have to have a website but you can have any e-mail sent to ANYTHING @ YOURDOMAINNAME . co . uk forwarded to a Hotmail account or the e-mail address your ISP gave you. You can pay extra to have an actual account set up with them but cheaper and easier to have it all forwarded to a Hotmail account instead. (This is what i do)
As you own the YOURDOMAINNAME . co . uk bit the first bit doesn't matter. Any mail sent to any address with the YOURDOMAINNAME . co . uk on it will come to you.