PM ("PM" ) gurgled happily, sounding much like they
were saying:

Mr B has said he is going to keep the car. Miss A's parents want it
back as part payment for the debt due. The car is at Miss A's house
and she holds the V5 and one of the two sets of keys.

But the V5C is in his name?

Yes - at her address.

Sorry, I'd missed that the car's actually at her place. So she's got
everything bar the name on the V5. Small but vital difference. I assumed
he'd taken it with him and was using it as his. In that case, I think I'd
definitely be getting it re-registered. The V5C is still at her address,
so he's not going to get a chance to object.

Who owns the vehicle?

No way to be certain without it going to court, but I'd say that Mr B
had the strongest claim at the mo.

That is, of course, not the answer that Miss A's parents want to hear

See above. Possession is 9/10ths... grin

Can the vehicle's registered keeper be re-assigned to be either Miss
A or Miss A's parents - none of whom drive - without the consent of
Mr B?

Registered Keeper is, as DVLA take every opportunity to remind, nothing
to do with legal ownership. They can apply to get a V5C in their name,
but Mr B will get a letter from DVLA saying "Do you agree?". If he
agrees or ignores the letter, they'll eventually get a V5C through. But
they still won't HAVE the car...

Miss A has the car at the moment, and it has been immobilised so Mr B
can't use his key. However, he'll have contacts with low loaders - and
low scruples - if he really wants it back.

Mmm. Definitely move it.

If they use those spare keys to "reclaim" it, then Mr B is going to
ring plod and report it nicked. Since his name's on the V5C, they're
going to go with that.

He'd have to get insurance first...

Even better. For them.