I don't think we have a specific word in BrE for protestors who climb tall structures in order to hang banners, paint slogans or simply to hang out at the top to get some publicity.
There are people who climb very tall structures merely as a challenge (usually illegally). I think they are referred to sometimes as "extreme climbers". The people who climb very tall structures and then jump off, using a parachute to save them from a splatty end (by the way, I made up "splatty") are called "BASE jumpers". The acronym "BASE" comes from the first letter of "building, antenna, span and earth". "Span" means "bridge" and "earth" is apparently used to denote a cliff. Those are the four types of structure that BASE jumpers jump off. Quite a lot of them die - according to Wikipedia there is one fatality for every 60 jumps.