Tthis is the easiest way to think about it:

Whatever finance you have at the moment can't be swapped [it's a loan secured on that particular car].

If you owe £11k to the finance company, you sell it for £10k, thats a £1k short fall [plus any penalty payments for early settlement].

You want a car for £5k.

You want to borrow £5k from a finance company to buy the car.

You still owe £1k for settlement on the other car.

£5k + £1k = £6k to borrow.

In reality, thats all done there and then, there's obviously no bridging period.

Thats the idiots guide , but any salesman will be able to sort it for you in one fell swoop