First and foremost you should use Domain Name Search to find a good domain for your directory. For a UK directory, try to get a .co.uk domain. Domain checker can tell you if the domain is available or not. I just checked and domain-directory.co.uk was available and I could buy it for 2 years for 10 pounds If you want to try multiple domain options, go to Bulk Domain Search.

You own a domain but that’s not enough, you need to get Web Hosting, preferably from a UK based hosting company (if you haven’t figured out, I recommend VelnetWeb). I personally like most economic starter packs that allow me to experiment with new websites without spending a lot of money. If you plan to host multiple domains or expects a lot of traffic on your websites, go for a bigger hosting plan.

You had a good brandable domain and hosting for your directory, all you need is to upload install your directory script.