A GRADE II listed summer house at Rivington Terraced Gardens has been destroyed overnight.
It comes at a time when pathways leading through the gardens to Winter Hill remain shut off to members of the public.
However, staff and volunteers at the heritage site say they have been challenged aggressively by people trying to gain access and arguing that the fire is out.
Overnight on Wednesday, the summer house at Rivington Terraced Gardens was broken into, with vandals causing more than £1,000 worth of damage.
Andrew Suter, Heritage Projects Manager at Groundwork CLM, said: "The damage to the structure itself is quite extensive. They have broken into the site and pulled the door off.
"We think they have taken the opportunity, while the grounds are quiet, to cause damage. They have taken advantage."
The summer house, which sits on the great lawn in the gardens, was used by Lord Leverhulme for entertaining. It is being restored as part of a £2.5 million Heritage Lottery Fund Parks for People programme.
At the end of July, vandals also cut through a lock on the gate at Lower House car park to gain access.
Signs and posters asking residents to stay out of the area and lengths of police cordon have also been pulled down.
Mr Suter said: "The area is still closed off but sadly lots of people have decided for themselves that the fire has gone out.
"Last week, the fire service asked us to do more to stop people gaining access so we have installed locks, put barriers in place and put signs up. We have also been patrolling and asking people to stay away.
"We have seen people of all ages climbing the fence, determined to get in.
"It is frustrating for everyone because clearly it is human nature to want to go up and see. But this is still an incident that the firefighters are actively tackling.
"People need to respect those who are asking them to stay away."
The team who manage Rivington Terraced Gardens is due to meet with the fire service on Monday to decide when the gardens will be reopened to the public.
A spokesman from Lancashire Police said: "We were called around 11.10am on Thursday following reports of a burglary in Rivington.
"An outbuilding had been broken into off Rivington Lane."
Anyone with information should call police on 101, quoting crime reference SC1807223.
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