As far as I know (from talking to my postman, as I was also curious), there is nothing sophisticated about it - no machines etc - mail goes through the system normally, and the delivering postman has a list of which address/surname combinations are redirected, and he takes those letters back and they are sent to a redirection centre.
Note that it's not an address that's redirected - it's a combination of surname and address - you have to pay per surname - I recently moved and I think it was about 17 pounds per surname.