That's going to be expensive. St Catherine's Dock
? Marina if you want to try a google
Right by Tower Bridge (The Lifting One) and currently with several Thames barges and only one Cat in there. Loads of big, wobbly plastic stuff too. Cam full by appearance.
If your mast
dismounts there are good canal boat type moorings on the Thames up Tolworth way, a mile or so inside the M25 on Google Earth
OR Southampton/Portsmouth are an hour away from the City by fast train.