So everytime you sell, you must return the log book ?

In theory that's supposed to happen here too. But when you buy it again, you can just apply for a new log book saying you never received the old one, or it was lost/stolen etc.

But you telling them it is sold ( in writing ) is enough to remove your liability for it. What the "buyer" does with it is then their problem.

Although I guess if you wanted, there are plenty of empty or derelict houses about you could use as an address. I see them daily when driving about.