Singlepage does not offer domain name registration as a service - you should register domain names with a reputable domain name registrar.
When you are registering domain names, make sure you choose a domain name registrar that:
Nominet is the official body in charge of .uk domain names and there's a lot of information on their web site:
Go to the website of your chosen registrar and go to the "Domains" or "Domain Names" page. You should then be able to search for the name you want, to check that it hasn't already been registered by someone else. If your chosen name is available, you should be able to register it. Each registrar will have their own process, but it is like buying a product from an e-commerce site - you will add the domain name to your shopping basket and then go through a process for setting up an account and paying. As mentioned above, Direct Debit can be better than paying by debit/credit card, because card payments can fail in future years when the card may have expired or been replaced.
Registrars will usually try to sell you lots of other services such as web hosting and email at the time you place your domain name order, but you should say "No" to these options and just get the domain name registered.
You'll get some login details and a password when you first set up an account with a registrar. Make a note of these details for future use because you will need them when you're ready to put your new web site live.