If the domain name you want has already been registered by someone else, you have a couple of options (other than coming up with another domain name).
You can use the Nominet WHOIS lookup tool to find out who currently owns that domain, and then get in touch with an offer to purchase the domain from them. Make sure you do your research first to determine whether the domain name is currently being used, and if it has an associated brand identity. This will influence whether the owner will be open to selling and how much for.
If you feel you have a right to the domain, potentially through a registered Trade Mark or contract agreement, then you can use our Dispute Resolution Service. You can find more information on this service on the Nominet website.
To find out who currently owns a registered domain you can use our Nominet WHOIS lookup tool.