Transferring .CO.UK and .UK domains are a bit different than traditional TLDs.
Rather than unlocking your domain, paying for a domain, and submitting the transfer (like you would with most TLDs such as .com, .net, and .org), you have to have your current domain registrar update the ISP Tag.
Please have them change the ISP Tag to:
Once this change is completed, please submit a new ticket to inform our domains department.
They will add the domain to your account or provide further instruction on what you need to do.