If it has been more than 24 hours I would recommend asking 123-reg to confirm the transfer has happened correctly and the correct IPS Tag has been used. If it has been less than 24 hours then just wait.
On a side note when you say that it hasn't disappeared from Fasthosts and appeared in 123-reg are you looking at the domain name part of the control panel or the hosting part of the control panel. You can configure any host to work with any domain name, in theory I could setup an account with Fasthosts to answer to "www.google.com", however seeing as the DNS entry wouldn't point to it no pages would ever be requested.