Sheffield is one of only two cities in the region not to have introduced the initiative, which entitled over-60s and under-16s to swim for free at local authority-owned pools, in April 2009.
The Government provided 140m to improve swimming facilities and also meet the cost of providing free access to pools.
But Liberal Democrat councillors in Sheffield said the initiative was a "sham" and the cash provided would not have been enough to cover the cost of implementing the scheme.
They claimed local taxpayers could have faced a bill of up to 1.5m, as the grant the Government offered fell far short of what was required.
Figures obtained by the Yorkshire Post under the Freedom of Information Act, however, showed that where the scheme has been introduced the cost has been far less than the figures quoted by Sheffield Council and, in most cases, councils have managed to fund the free swimming entirely from their Government grant.
At a full council meeting on Wednesday Councillor Jackie Drayton will propose a motion calling on Sheffield Council to reconsider introducing the scheme and also confirm that Labour will take up the funding if elected into power in May.
Coun Drayton said: "I'm shocked that the Lib Dems have been so stubborn in their opposition to free swimming.
"Free swimming for under-16s and over-60s is available everywhere else in South Yorkshire and in most places across the country but not in Sheffield.
"The Lib Dems have ignored reassurances and personal invitations to join the scheme from three Government ministers, as well as ignoring a 3,000-strong petition and some brilliant research by the Yorkshire Post proving it wouldn't cost much at all.
"Labour have listened to Sheffield residents and they've told us they want free swimming, just like they have everywhere else across the country. That's why we're promising to introduce free swimming if we get elected in May."
Nationally, more than 300 councils took up the funding and, in Yorkshire, the figures show every council that implemented the scheme has seen a dramatic increase in the number of participants.
In Barnsley, prior to the scheme being introduced, an average of 16,350 under-16s swam each month at the authority's leisure centres, which has since risen to 22,706. For over- 60s, the figure was 1,368, which has since risen to 3,071.
In Bradford, the number of under-16s swimming each month has rocketed by more than 10,000 – from 19,007 to 29,189. Meanwhile, the number of pensioners swimming has almost trebled, from 2,348 to 7,054.
In Leeds, the average number of swims has soared from 21,082 to 27,727 for under-16s and from 8,165 to 10,746 for over-60s.
Councillor Sylvia Dunkley, Sheffield Council's cabinet member for culture, sport and leisure, said: "We always said that we wanted to take part.
"However, when given the choice between taking part and delivering the lowest ever council tax increase in Sheffield we chose the latter, which I think was the right choice given the current economic climate.
"Despite this we have been able to do our own swimming scheme which involves providing hundreds of local people with low-cost swimming lessons.
"As a result, hundreds more people in Sheffield can swim and 97 per cent of them have gone on to become regular swimmers."
Wednesday's full meeting of Sheffield Council takes place at 2pm at the Town Hall.