Mr Heald said: "I have written to both our local councils to press the case for measures to safeguard the cave."
Crucifixion wall carvings
He added: "I believe that there should be a weight restriction and strict enforcement of the no parking provision, so that we can save the cave."
Chief Executive of English Heritage, Dr Simon Thurley, has recently written to Mr Heald to confirm that "potential long-term damage due to the weight and vibration of continuing heavy traffic is of concern to us".
The cave is a man-made cavern in the shape of a beehive, with a small aperture at the top for ventilation.
Inside are wall carvings representing the Crucifixion, the Holy Family and several saints, including St Katherine, St Laurence and St Christopher.
Local historians have said the wall carvings suggest the cave may have been used by the Knights Templar.
The Knights Templar, a military order of the Roman Catholic Church, were suppressed by papal edict almost 700 years ago.
Royston Cave is managed by the Royston History Society on behalf of Royston Town Council.