Logically, it has to be a weekday - if they do it on a Saturday/Sunday - none of the council office bods will be around to see it, nor the London Assembly peeps or anyone else.
And they do arrange it for lunchtime, so if you're already working in town, you can take a lunchbreak and join in. If you don't make it back to work in the afternoon, it's probably because you got caught up in the protest and couldn't get back to the office, sorry boss