Try the excellent https://dronescene.co.uk
Turn on these three layers: Airspace Restrictions, Flight Restriction Zones, and NOTAMs.
Keep clear of the obvious Airports (Heathrow and London City Airport among others) and Heliport.
Keep clear of the Heliroutes (yellow snakes), Broadly speaking they are designed to keep helicopters over the Thames.
Read the NOTAMs (usually but not exclusively blue circles) and see if the dates and altitudes affect your plans.
It’s considered the big area called “The Specified Area” affects helicopters and not drones.
And then you’re just looking for a from which to take off that suits the weight of your drone (use Where can I fly my drone in the UK? - Good 2 Go - Can I fly my drone here?). Don’t use Royal Parks (there’s a special exception for an area in Richmond Park if it wouldn’t bother the deer there)
Taking most of that in to account, there lots of places to fly.
I TOALed from the green spot in one of these two photos:
All this info gleaned from searches of this forum.
Late addition: watch out for signal interference, and don’t rely on Return To Home feature (from a post a couple of weeks back)