Labour and Liberal Democrat members of the London Fire and Emergency Planning Authority have criticised a proposal to shut the London Fire Brigade Museum.
Three years ago a similar proposal was withdrawn after objections were raised by serving and retired firefighters, unions and museum users.
So far more than 1,100 people have signed a petition calling on the authority to save the museum which costs just £81,000 a year to run.
"I believe that the whole proposal is ill-conceived," said Cllr Navin Shah AM, a Labour member of the fire authority. "This is our heritage and history we are talking about."
Cllr Shah was speaking at a meeting of the authority's finance and personnel committee on Monday morning.
"The right approach would be to look at how we can invest in a more accessible, better museum which can enhance the educational aspects ... rather than losing the entire collection at a stroke."
Cllr Shah added: "This should be off the agenda. We should look at how we can safeguard and enhance the provision. I thought that the Mayor's proposal for a blue light museum was a good one ... but obviously that has disappeared in smoke."
Cllr Terry Stacy, a Lib Dem member of the fire authority, said he understood the need to make cuts but warned that the museum closure and other proposed savings would "allow resentment to build among staff and the community as a whole".
"There's a lot of huffing and puffing about the museum," Brian Coleman told the committee.
He explained that the future of the museum would have to be considered in the context of plans to outsource the training of firefighters which is currently carried out at the Southwark Bridge Road site.
"In the medium term Winchester House and the whole Southwark [training centre] site will go," he said. "It will have to be disposed of. When [the site] goes, there's no space for the museum.
"I wish we had money to invest in the museum. I wish we didn't have to make the various cuts ... but I see no proposals from the Labour group on how we can make up this deficit bearing the mind the cuts target we have been set by the Mayor which is part of his political directive to freeze the precept for Londoners."
Cllr Coleman added: "I would be happy to reverse the proposed savings if Cllr Shah could propose other savings or other sources of revenue."
Turning to the proposal for a combined museum of London's emergency services, Cllr Coleman said: "It was actually my idea, worked up with the late Sir Simon Milton, to have a blue light museum, and [the Mayor's culture advisor] Munira Mirza spent £8,000 of taxpayers' money on getting a consultant in to look at it. I'd have done the exercise for 10 per cent of that fee.
"I understand that the police wouldn't play ball – as ever – because the key attraction for a blue light museum would be the so-called 'black museum' from Scotland Yard.
"They queue round the block for the London Dungeon and I think they'd queue round the block for the contents of the 'black museum'.
He continued: "There's the London Ambulance Service Museum out in Ilford and several warehouses – which you are paying for – to store old police vehicles, believe it or not."
"I still believe that there is some merit in the blue light museum."
The proposal for the closure of the museum – and the overall draft budget for the fire service – will be considered at a meeting of the full authority on Thursday 24 November.
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