Maybe I should say "Even Londoners might not know every place."
I'm speaking of the Royal Park "Isabella Plantation" - a wonderful park in Greater London, and maybe you should wait a few weeks, but the first azalea on my balcony has opened her tiny buds and tries to envelope herself in a veil of fragrance (though today the weather changed: from 20°C yesterday to 7°C now.).
I visited the Isabella Plantation last year in my monthly stay in London end of May. Everything was still flowering, but on the verge to vanish. It was Trish, (my sweet landlady and now my friend) who told me about it - in her long life she hadn't been there, but heard about it.
And it was marvellous! The long way from the station and bus station was a bit -- very solitary -- but as an 'Urban Warrior' I wasn't that worried. And you can go there by car. It is in Kingston upon Thames.
It is a huge park, mostly rhododendron and azaleas, some very old ('Planted in 1831' reads the plaquette beside a huge rhododendron), and beautiful little brooks.
Then follows a heather landscape with a big pond.
Find the time - plan to go there - it is really worthwile, because gardeners and nature are giving their best - nature even as a florist.