You are right under the flight path to LHR (London Heathrow) and near heliports.
With the security around London, I would advise you NOT to fly your drone, as the outcome could mean problems.
There will be lots of places you can fly your drone in London. I can only imagine how many drones are owned by good pilots/people and are used without incident every single day. Maybe have a look at some of the main flight clubs London has to offer and see where that leads you? That's what I would do, plus there are some incredible and large parks there which you could fly in, again these clubs will know the deal.
Great information
The OP was asking about "tourist places" so one must assume "somewhere near London".
As you suggested good link to clubs that will know where to fly the drone.