Someone's just advertised a boat for sale in central London, with mooring included. The boat's a 45ft trad narrowboat, built in 1985. It's highly unlikely to be worth much over £25,000, and the £70,000 asking price probably reflects a hefty premium for the mooring.
It's conventionally said that before you buy a boat, you should look for a mooring. Not really true; it's easy enough to find moorings around the country. Depends how fussy you are about the boat's location.
But London's moorings - inevitably - come at a tremendous premium, and residential ones even more sought-after. Mike Stevens gives a useful summary on available residential moorings.
The most famous and expensive (because they are so photogenic) are at Little Venice, near Paddington, but there are moorings stretching along the Grand Union Paddington Arm, the Regent's Canal and parts of the River Lee that would qualify as 'Central London'. Don't expect them to be cheap. The £70,000 boat+mooring probably won't even buy you the mooring - it'll just be the right to pay the ongoing mooring fee, which could well be another £5,000 per year.