While there is an Auth/EPP code needed for most domain transfers, when it comes to .co.uk domains, it is required to change an IPS tag.
That can be done by contacting your domain registrar (the company that you purchased the domain from). They need to set your domain’s IPS tag to REGISTRAR-EU so the transfer could proceed. After that, just follow this article, which will guide you through the domain transfer :)
NOTE: You can also click here and find out how to transfer different domains with EPP/Auth code.