How long do I need to wait until an expired .uk domain will be available for purchase?

When a .uk domain expires it will eventually become available for someone else to register.

Expired .uk domains are available for re-purchase 90 days after the expiry date of the domain, if not renewed by the current domain owner / registrant.

You can perform a WHOIS lookup on any .uk domain via the Nominet WHOIS service in order to check the domain’s expiry date.