A council chief fears Buxton's Pavilion Gardens could change 'beyond recognition' if the attraction is 'offloaded' to the private sector.
As part of a tendering process, High Peak Borough Council is currently inviting applications from 'suitable operators' to provide hospitality, catering and events services at the Pavilion Gardens.
The Tory-led authority insists the proposed move would help to safeguard the historic venue and protect jobs.
But Councillor Anthony Mckeown, leader of the Labour group on the council, said: "News that the operation of the Pavilion Gardens is being put out to tender to the private sector to take over will be a cause of concern to many residents.
"Those concerns will be further heightened as the tender goes far beyond previous plans and now covers the entire Pavilion Gardens operation, including all of the buildings, the miniature railway, bandstand and park kiosk – with everything all effectively up for grabs by the private sector.
"With a potential contract life of up to ten years, this tender has the potential to significantly change an iconic part of Buxton beyond recognition.
"The Labour group will work to scrutinize any proposals submitted to ensure that before the council moves forward to 'offload' the Pavilion Gardens the voice of residents is heard and that any proposal is right for our staff working in the gardens and residents in Buxton and the High Peak."
Coun Tony Kemp, executive councillor for tourism and regeneration, responded: "I am disappointed by Coun Mckeown's attempt to politicise this process since the current administration has been entirely transparent about the whole issue and made clear for years, rather than months, that this exercise to explore the potential to outsource the Pavilion Gardens operations would follow the completion of major repair work to the fabric of the heritage buildings.
"The council has little choice since the net cost of running the complex is enormous and, although we made sterling efforts to improve gross profitability following the cafe, retail shop and arts centre refurbishments, we could come nowhere close to just breaking even.
"The enforced closure of the Octagon and the resulting impact on business throughout the complex has pushed us well back.
"Coun McKeown is very well aware that councillors of all political persuasions, and from outside Buxton, have been most dissatisfied with this position for many years, irrespective of who has been in control at the time. Nor have I heard any serious alternatives put forward by the Labour group.
"I'd like to make it clear that safeguarding jobs is firmly at the heart of what we are doing, not just cutting the cost to the council taxpayer across the borough.
"Political control changes, as does the distribution of councillors between the wards - and we live in a time when all national parties seem set on getting rid of smaller authorities like High Peak and shifting control of local services away from local people.
"To be blunt, my greatest fear is that at some point in the future, and if we do not get the cost of the Gardens under control, then the doors will simply be closed to save money.
"Where will the jobs and our much-loved facilities be then?
"I don't consider there has been 'mission creep' as Coun Mckeown suggests and in any case the process has and will continue to be fully open to scrutiny by elected members, so he is suggesting nothing new. Staff have been kept informed of matters at all stages and will continue to be so."
The intended start date for the contract is January 1, 2019.