I've got my (new style) registration document in front of me and I can't see anywhere that the DVLA ask about the ownership of the vehicle.
Perhaps an example might make things clearer:
John Smith drives a company car owned by Bloggs Ltd. The registered keeper will be John Smith, not Bloggs Ltd.
Bloggs Ltd then get taken over by Acme Widgets who allow John to keep his company car. (So, John remains the registered keeper).
Later on, Acme Widgets transfer their company cars, through a lease-back agreement, to Cheap Fleet Leasing (but still permitting John to use the car as his company vehicle). John, therefore, remains the registered keeper.
The car will have had three different owners but the registered keeper, John Smith, will not have changed and nobody will have needed to notify the DVLA.
The DVLA has no interest at all in who actually owns a vehicle. They only want to know who the registered keeper is and, as it says within Section 5 of the registration certificate, "the Registered Keeper is not necessarily the legal owner".
The DVLA aren't interested in who owns the vehicle of your friend's late father. They only want to know who the registered keeper is. (If, for example, your friend decided that he wanted to retain ownership of the vehicle but allow you to keep the vehicle at your house and be the person who drove it for most of the time, it would be you, and not your friend, who would become the registered keeper even though you wouldn't be the owner).
Chris