The youths scaled a fence on Sunday teatime to get into the park which had been closed for weeks due to the foot-and-mouth crisis.
After failing to break into a storeroom on the Scouts' campsite, they set fire to the kitchen and attached classroom.
"I am very disappointed for the children who use the site," said Dave Metcalf, Scout District Commissioner .
"Many of our visitors are from deprived areas and this is their only chance to enjoy the countryside."
The blaze - started at about 6.30pm on Sunday - was spotted by a caretaker at his flat in the mansion.
Ranger Tim Birtles was one of the first at the campsite which last year welcomed 3,500 children.
"It was well alight by the time I got there," he said. "I could see the extent of the fire from a distance."
Knutsford firemen spent three hours at the scene because all their equipment, including clothing, had to be sprayed with disinfectant before they could leave.
"We were unable to save any of the building or its contents," said a fire spokesman yesterday.
Plans to improve the site had been cancelled due to foot-and-mouth disease.
"We were ready to open as soon as the park re-opened, but now we may have to let more children down to sort out the damage," said Mr Metcalf.
The wooden building and its kitchen have been valued at £60,000. A replacement is unlikely to be built.
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