To transfer your .UK domain name from iwantmyname to another registrar requires changing what's called the registrar tag or IPS tag to the new company's tag. It works a bit differently from gTLD transfers, like for a .com domain.
Login to your iwantmyname account, and go to this page:
https://iwantmyname.com/dashboard/domains/edit/<< domain.tld >>
Click transfer to another registrar. On the next page, type in the new registrar's IPS tag in the field provided. If you're not sure what their IPS tag is, the new registrar's support team can provide it to you. Ours, for example, is "1API-DE".
Click the red transfer button to initiate the transfer. Once that's done the transfer will automatically complete within an hour.