There was a time when you could not buy a .uk domain if the .co.uk domain had already been bought by someone else.
The Nominet Registry launched the .uk top level domain (TLD) in 2014. Anyone who already owned the .co.uk, .org.uk, or .me.uk version of that domain had the preferential right within five years to register the .uk domain.
That right ended on 25th June 2019 and now anyone can simply choose to register the .uk domain even if someone else owns one of the other members of the family of uk names.
List of Internet top-level domains
The original TLDs were .com, .org, .net, .int, .edu, .goc, and .mil. There are now man more that 1,500, which you will find listed by the Internet Assigned Numbers Authority on this page.