London WNBR has a photo policy page https://wnbrlondon.uk/wnbr-london/need-to-know/photography-policy/ which notes that:
This protest takes place on the streets of London and attracts many professional and amateur photographers and film makers. As such, we are not in a position to enforce policies, conditions or restrictions. As a campaign, we welcome and support positive media coverage. We also recognise that many of the participants want to keep or share their memories. Inevitably, the general public will reach for their camera phones as the ride goes past.
It continues:
We do not welcome images of people undressing, dressing or standing around waiting – these miss the point and appear exploitative.
So generally, no specific ban, but a strong discouragement — which indeed is all that’s legally possible in an open area of a public park.
The Croydon start point is different, because unlike most of the other start locations in public parks, this is in the grounds of a private residence:
The location is a gated, private residence, so you will be able to relax and prepare for the ride in privacy. Although supporters and friends are welcome to enjoy the 2 acres of clothing optional gardens, our policy is to deny access to photographers and gawkers.
There is nevertheless an invitation for genuine press photographers to attend the Croydon start and take photos with permission of agreeable subjects and a requirement to obtain model release from them.