Illegal vehicle users have also been using winches to damage trees around the Dudmaston estate, which causes the ground to be ripped up, say officers at Bridgnorth safer neighbourhood team.
A spokesman for Bridgnorth SNT said: "We have been made aware that there has been a rise in illegal use of off-road vehicles around the Dudmaston area. These offenders do not have permission to drive on this land.
"They are using winches to damage trees which causes the ground to be ripped up. They have also broken through a gate to get out of a field. This is all criminal damage and when we find out who the offenders are we will prosecute them."
Police also say that the National Trust works hard to keep the land nice for its visitors.
"Please contact us if you see any of these vehicles in this area. If you can make a note of the registration this will really help us bring offenders to justice," they add.
The Dudmaston Estate is at Quatt, near Bridgnorth and extends either side of the A442 between Bridgnorth and Kidderminster.