There are bookable visitor moorings in Paddington Basin, Little Venice, Islington and Kings Cross. Some are £25 per night and some £35. There used to be some in Camden but the London boaters complained too much and they have reverted to normal free moorings. The Islington and Kings Cross moorings have hookup points and you need to set up a MeterMacs account to use then. Nearly all other moorings in London are 14 days, they do not become 2 days in summer. You'll probably find a free 14 day mooring but you are likely to have to brest up or be brested up to, there's no asking if this is ok it just happens.