Ministers have been accused of a “stitch-up” over proposals to redraw the funding formula for councils in a way critics say will redirect scarce cash from deprived inner cities to affluent Conservative-voting shires.

The proposed changes – which include the recommendation that grant allocations should no longer be weighted to reflect the higher costs of poverty and deprivation – come amid increasing concern over the sustainability of local authority finances.

Leaders of urban councils have written to ministers to complain that under the “grossly unfair and illogical” proposals, potentially tens of millions of pounds would be switched to rural and suburban council areas.

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Cllr Richard Watts, the leader of Islington council in London and chair of Labour’s local government resources group, said: “The evidence used by the government to justify these changes seems so bizarrely selective that it’s impossible to avoid the conclusion that the review is a brutal political stitch-up aimed at sparing Tory councils and Tory voters from more cuts while piling misery on the most deprived areas of the country.”

He added: “Only this government would think it is fair to cut money from the communities that need it most to give it to well-off areas.”

Northern cities and metropolitan councils see the so-called fair funding review of local government revenue grant funding as an attempt by ministers to prop up financially struggling authorities and declining services in Tory heartlands. An estimated 76% of Conservative MPs represent constituencies covered by county councils.

The financial collapse of Northamptonshire county council a year ago – and well-publicised difficulties faced by other Tory-run counties such as Somerset and East Sussex – have focused attention on the impact of austerity cuts to local services such as libraries, parks and Sure Start centres in even relatively affluent areas.

Details of the proposed changes were contained in a consultation released by the Ministry for Housing, Communities and Local Government just before Christmas. The ministry has insisted the review is a technical exercise designed to simplify grant distribution among English councils and will make the process more transparent.

But critics believe ministers have bowed to pressure from the Tory-dominated County Councils Network to shake up the grants system. The CCN has argued its members are unfairly allocated less money per head of population than inner-city areas, and face higher costs of maintaining services in sparsely populated rural areas.

Sir Stephen Houghton, the leader of Barnsley council and chair of the Local Government Association special interest group of metropolitan authorities, said the removal of deprivation from the proposed formula was absurd and unacceptable.

He said: “The credibility of the whole review is – in my opinion – at stake, as I am not sure how the ministry will be able to justify that services such as waste collection, street cleaning, homelessness, public transport and libraries are needed solely on the basis of population numbers no matter where you live.

“If you are an affluent homeowner who also owns a car and computer and has money to spare, I cannot see how that justifies the same council resources as someone who potentially may not have stable accommodation, relies on public transport to get around and on computers within local libraries to access welfare.

“Not only is it grossly unfair but it is illogical. Any finance officer will tell you that the cost of providing services in their borough increases in their more deprived areas due to demand and as residents are less able to finance their needs themselves.”

Cllr Nick Forbes, the Labour leader of Newcastle council, said the proposal amounted to an “act of war” that was designed to underpin the finances of largely Tory-controlled county and district councils at the expense of the inner cities.

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“The change would be to the serious detriment of urban, economically and socially disadvantaged areas, which also mainly happen to be Labour-run council areas. It’s utterly mendacious,” he said.

London Councils, the body that represents the capital’s 32 boroughs, has signalled its opposition to the proposed new formula. It argues it is more expensive to run services in areas such as London that have high deprivation, high salary and building costs, and a rapidly growing population.

Traditionally, the distribution of revenue resource grants to councils has been weighted in favour of poor areas because deprivation is seen as a driver of higher than average demand for social care, housing, and other neighbourhood services. It has also been recognised that poorer areas are less able to raise taxes locally.

However, the proposal would remove deprivation from a “foundation formula” that covers funds for waste disposal, public transport, libraries, leisure, planning, homelessness and recreation – together amounting to about 30% of a council’s budget. Cash would be distributed purely on a population basis – with an added weighting for the costs of rurality.

Deprivation would be retained in separate formulas for adult social care, children and youth services, public health, highways maintenance, flood defence, and fire and rescue services. The new social care formulas have yet to be unveiled.

Cllr Jas Athwal, the leader of Redbridge council, said: “Outer London boroughs like Redbridge already have some of lowest levels of funding in the country. With a rapidly growing population and significant areas of deprivation, we face £50m of cuts in the next three years. We need to ensure that our residents shouldn’t have to take even more pain to bail out the shires.”

A spokesperson for the Ministry of Housing, Communities and Local Government said: “ We have launched a consultation seeking views on what factors to include in a new funding formula. This is a complex piece of work and we will take the time to get it right. We have been clear that this is a review of the relative needs and resources of local authorities.”