I have just gone through the exercise with Ofcom.
1. Original owner of vessel [person who has licence] accesses the licence online and `surrenders' the licence.
2. The original owner informs the new owner of the MMSI and the call sign.
3. New owner accesses the licence online, using the MMSI and call sign.
4. New owner registers their details against the original licence number, MMSI and call sign, as they are all issued for the vessel not the person.
You can do it using old fashioned paper and Royal Mail, but unless you are over 75 years old Ofcom will charge you £20 for the priviledge. Online it is free for life.
Once the info has been recorded by Ofcom, it is their responsibility to inform IUT of the change of ownership to go on MARS database!
I hope that is all clear. If not, Ofcom are quite helpful if you telephone them 020 7981 3131.