Nominet, the Registry for .UK TLDs requires you to add the so called IPS tag to the OLD registrar.
Initiate the Transfer at the Current Registrar with whom you are managing your .UK domain name. You need to provide the IPS Tag of the Gaining (New) Registrar in order to initiate the Transfer.
The HelpingHost.com IPS tag is: PDR-IN
When done, you can start the transfer process here.