Where can I buy a whole salmon in London?

[Mummalish]

And not too expensive? Do supermarkets do them?

Supermarkets with a fish counter usually sell whole fish.

Yep - most supermarkets fish counters will order you one in - Waitrose will loan you a fish kettle to cook it in.

John Lewis foodhall. They will often have a fish kettle for you to hire too.

Billingsgate fish market would be the best place if you don't mind an early start. Open from around 5-8am.

If you've got a supermarket with a fresh fish counter, talk to the fishmonger.
Round here, they are only out easter and christmas etc, but I'm sure they could get one for you