The two popular visitor attractions had been earmarked to shut in early discussions by Peterborough City Council leaders in a desperate attempt to shore up local authority finances.
The council is under pressure from the Government to get a grip on its escalating financial crisis which has seen the difference between income and spending rise to £27 million.
Both the Museum and Art Gallery, in Priestgate, and the Flag Fen Archaeology Park cost the council £600,000 each a year.
Announcing the details of the council’s budget for the next financial year, which includes £12.6 million of spending cuts and a 2.99 per cent Council Tax hike, council leader Councillor Wayne Fitzgerald said: “I’ll be honest with you.
“The original suggestion was to close the museum entirely and close Flag Fen entirely.
“And we had to step back front that and say that it would be a difficult thing to do - both on a political basis and also would it be right for the people?
“So that is why there is a reduction in spending.
“It is the same with the libraries.
“We have a statutory duty to provide some services but not to the level we’ve got currently, which is why there is a review.
“But we could have easily closed some things but we not doing that.”
The council’s budget sets out ways of making £1,431,000 savings in its cultural and leisure provision.
It currently spends about £2.6 million operating the museum and art gallery, libraries, the Key Theatre and Flag Fen, gyms and leisure centres, the regional pool, and the Lido.
The budget states: “Our aim, as part of the need to get the council to a stable financial position, is to deliver culture and leisure services at net zero cost to the council.”
It proposes to cut the amount the council pays City Culture Peterborough, which operates the Peterborough Museum & Art Gallery and Flag Fen, by 50 per cent.
It states: “This will require City Culture Peterborough to review how the facilities operate, which will likely see a reduction in opening times for both sites.
“The review will also investigate how the attractions could generate more income.”
The council also hopes to remodel the city’s library service.
Currently there are 10 libraries and a mobile library service operating across the city.
The aim is to modernise the library service so it costs less but also to invest in the mobile service and digital resources.
The document states the council’s goal is to explore the benefits of having a charitable partner which if implemented could release both VAT and business rate relief of between £500,000 and £700,000 a year.
Details of the escape from closure of the museum and Flag Fen come after the council announced the closure of Peterborough’s Key Theatre, on the Embankment, only to quickly reveal the venue had been saved with a five year deal with Selladoor, which also operates the New Theatre on Broadway.