I'm not going to do that, but one that especially interests me is The Barbican. At any time of year the Barbican is always a treat to go through with it's gardens. When I worked in London that was one of my little bolt holes, not only when going to a concert or other event there.
I think the garden participating at The Barbican is usually residents only. They have a "Garden poet" in attendance.
https://londongardenstrust.org/log2025/gardens/BarbicanW.html
The Barbican Conservatory is worth a visit outside of this event too. I didn't realise public opening was quite restricted. I've only been the once several years ago and it must have been on a public opening day by coincidence. You can check dates here -
https://www.barbican.org.uk/whats-on/2025/event/visit-the-conservatory
There's quite a few of these sites off the beaten track in London in some more unusual postcodes. I've put it in my calendar to see if I fancy visiting a garden listed anyway. Almost every one has some sort of interest.
One last one from me is new for this year - Moat Community Garden at Millbank on the historic Millbank Estate. It seems to be a collaboration between Tate Britain, Chelsea College of Art and residents on the estate. Some activities planned for the weekend.
https://londongardenstrust.org/log2025/gardens/Moat.html