At the annual meeting of the council Labour group leader Brenda Smith warned that the cost of the project could spiral to £3m.

She said: "There are examples from across the country where councils are pursuing new builds at relatively little extra capital cost, not least because the subsequent running costs are significantly lower."

And Independent councillor Alan Jackson added: "The council needs to be pro-active, explore the potential of a partnership with the county council for a new pool on one of the town's school sites and sell the idea to them."

Conservative council leader Malise Graham said in reply: "We have started nothing and until we get the tenders back for the refurbishment of the Waterfield complex we will have no idea which route we should follow. There is a six to nine month window in which these important decisions will be made.

"I want a swimming pool for Melton and would welcome any offers of help, but one thing everyone needs to understand is that we cannot afford a flume pool. We have to be realistic."

The flume pool, one of three at the baths in Dalby Road, is currently out of bounds on health and safety grounds after a problem with the roof was discovered.

The council wants to convert that area into an expanded gym and fitness suite to help cap running costs and boost visitor numbers and income, a decision which has been referred to the Local Government Ombudsman by campaigners hoping to save the the flume pool.

Mr Graham said Waterfield costs each council tax payer £12.05 a year which was not sutainable and insisted the council's plans would make the complex fit for purpose and would be affordable.

He added that the council's finances were tight with its Government grant set to rise by just 1.6 per cent this year and 1.5 per cent for the next two years.

"We cannot afford to run a tourist information centre or flume pool and invest in our priority neighbourhoods and the new children and family centres. Rather than pay for failure we want to help people achieve their potential."

Mr Graham said that since the tourist information service was withdrawn from King Street and run out of the council offices each enquiry now cost under 50p compared to £8 previously.