So this Saturday is International Pillow Fight day.. a few years ago it was first held in Trafalgar Square and loads of fun.. however quite a few people brought along pillows with feathers (which you weren’t meant to), so the square afterwards looked like a total mess..
and then the following year the London authorities decided they needed close the main square for “cleaning” (yeah right)
This year they are even more strict and apparently have threatened legal action against people who were unofficially organizing stuff.
There is a Facebook group FocalLocal for the 2016 Pillow Fight but not sure quite what is happening there.. maybe in St James Park, but I also heard that something was going to happen in Victoria Park.
Good luck if you find anything out there.. but as with anything fun and unofficial in London.. it often gets closed down.