Weirdly, its actually EH that is responsible for the upkeep and care of Scheduled Monuments in the Peak. I assumed like you it was the Parks Authority, but my report to them about damage to Hordron's Edge circle was forwarded on to EH... I think its to do with statutory responsibilities etc...
Anyhow. Just had this back from EH:
Thanks for bringing this to our attention - please assure Alastair Ross and the Modern Antiquarian community that someone will be out to Barbrook II over the next few days to have a look.