I just discovered a little gem.
True, unless you're a Chelsea resident or Friend of the garden you need to pay to enter, but everything else about this place is wonderful.
It's a small botanical garden at the Southern end of Royal Hospital Road, right next to the river, hidden behind tall walls, and dating back to 1673. The garden houses over 5,000 different plants in small beds and ancient little green houses, a pond, two beehives, and - best of all - a little cafe. There's ample room to sit and enjoy a lovely home made cake with tea. Unless you prefer coffee or cappuccino, which is really good too.
If I'd spotted a fairy I wouldn't have been surprised. I didn't but I'll keep looking.