Public rights of way, or access land, which apply to getting to most of the summits in the G association, simply give you the right to travel along / through the area. They do not give you permission to stick around for any extended period of time, nor undertake specific activities. All land is owned by some person or organisation - so essentially it could be inferred that permission is required for a SOTA activation from every G SOTA summit.
Common sense tends to prevail. If your activity is short-term and low impact, and most importantly leaves no trace of your being there, then few would have a problem with it - the same for other such activities like photography, kite flying or a family picnic, none of which have explicit permission either.
As Butser Hill has public access, I personally would take the approach of undertaking my activation anyway, but not hanging around too long or using particularly large antennas or masts etc. If asked to cease and pack away, I would comply without argument.
This is my personal opinion and not any official view by the SOTA MT.