The .uk domain used to not be available directly. You could only register .co.uk, .org.uk, and a couple of other subdomains of .uk. Since 10 june 2014, direct registration under .uk is possible, but there's a reservation period for existing .co.uk and other .uk subdomain customers to claim their existing name on the .uk domain.

https://en.wikipedia.org/wiki/.uk

I don't think you can get just a .uk. I'm pretty sure it has to be .co.uk which is a few extra characters thus making it a bit unattractive. Also, I think only UK residents are allowed and have to be approved, similarly to how Canada's .ca works. I'm not 100% sure though.