This answer will explain how you can move domain names between 123-reg.co.uk accounts.
From the account holding the domain name
2
Click on the Internal option below Domain transfers in the Domain names section.
3
Click on the Start an internal transfer link.
4
Type in the username for the 123-reg account that the domains are going to.
5
Select the domain(s) that you want to move to the other account.
6
Click the Start Internal Transfer button.
7
Confirm that you really want to move the domain name to the new account.
In the new account
2
Click on the Internal option below Domain transfers in the Domain names section.
3
Choose to Accept or Deny.
Please note: Moving domains between 123-reg account holders is free.