Same thing happened to me there (might have been a different marina, across from Barbican but not through the lock?). Even greener then than I am now. Luckliy there were couple of marina guys to shove me back up to the berth in a rib. SO don't worry, sŁ%t happens. Better there than out at sea, where that keel will be much more welcome. Coming in and out of marinas even in (the usual) flat calm still scares the pants off me much more than anything else so far. Don't worry, it'll be fine and before you know it you'll be far from those tidal currents and all that getting up at 5am to catch the tide.
And agree with the other guys, slow using prop walk works.