You're right, I'm from Holland (near Rotterdam) and I know that we can expect rain.
But we will have a good time even if the weather won't cooperate.

Jan

I strongly recommend Kew Gardens ( on the Richmond branch of the District line)

Unparalleled plant collections, the largest glasshouse (in the UK / world, delights around every corner tree walk , japanese garden and farmhouse, a pagoda!,

Visit the Maids of honour tea shop , near the main gate to pick up a picnic lunch!,

https://www.kew.org/

https://theoriginalmaidsofhonour.co.uk/

Mention of Kew makes me think of Wisley, Royal Horticultural Society (RHS) HQ and garden. The problem is that it is a distance form the nearest railways. West Byfleet is easy to reach from London Waterloo, but from there to the RHS is over 1 hour's walk (although that walk in itself includes a lot of country.)

As 'my back yard' I second the North Downs. Access stations include:

Dorking, Boxhill, Gomshall, Woldingham, Betchworth

There's a Wildfowl and Wetlands Trust site is a 15 minute walk from Barnes station:
https://www.wwt.org.uk/wetland-centres/london

Steven B