To transfer most domains you only need to unlock the domain and get the Auth Code which you will need to send to the registrar you are transfering to.
This can be done within the Billing system as you have full control of your domain.
For UK domains contact US and give us the new TAG info so we can request the TAG change.
You will get two emails which will be to confirm the transfer.
One will be from the current regsitrar and one from the registrar you are transfering to.