The damage was caused on two occasions. The first being between Friday, 30 October - Wednesday, 4 November. The second being between Friday, 6 November - Saturday, 7 November.
Officers from Sutton's Safer Parks police teams believe the tracks were caused by a motorcycle - and consistent with a 'doughnut' manoeuvre.
Officers have increased their patrols are working closely with the club to catch the perpetrator.
Sgt Pat Dolan, of Sutton's Safer Parks Police Team, said: "Such behaviour is totally unacceptable and we want the public's help to tell us who is responsible. The offender will be dealt with robustly."
If you have any information contact Sutton Police Station on 101. Alternatively, contact Crimestoppers anonymously on 0800 555 111.