Rob Marsh, a paramedic, posted the photo and said: "Lockdown has failed epically in Cannock Chase again.
"You’d almost think there was a drive through KFC in the grounds..."
Police and fire chiefs have previously pleaded with residents to stay at home after a number of incidents of arson on Cannock Chase.
And Forestry England has urged people not to travel to its sites, including the Chase, in light of the Government advice to avoid all but essential travel.
The car park at Birches Valley has been closed as a result, as have all cafes and bike hire centres, after play areas and toilets were shut by Cannock Chase Council beforehand.
Police have also warned residents in Staffordshire to stay away from beauty spots in the county unless they live within walking distance.
People are now only allowed to leave their home to buy basics, exercise once a day or travel to and from work if they cannot work from home.