Labour says its analysis shows most of new £300m fund to ease funding cuts to local government will go to Tory-run councils

David Cameron has been accused of buying off Tory MPs threatening to block local government cuts, after it emerged that a new £300m relief fund will overwhelmingly help Conservative areas, including his own Oxfordshire council.

The extra cash was announced after up to 30 Conservative MPs were poised to revolt against the local government finance settlement, which is due to be put to a vote on Wednesday in the House of Commons. The funding was announced by Greg Clark, the communities and local government secretary, to the delight of Tory MPs.

A Labour analysis shows that 83% of the new £300m two-year fund will go to Tory-run councils, mostly in the southern shires. It found that the biggest beneficiary will be Surrey, which will get £24m, with £19m going to Hampshire, £16m to Hertfordshire, £14m to Essex, £12m to West Sussex, £11m to Kent and £9m to Buckinghamshire. Cameron’s county council in Oxfordshire will get an additional £9m to ease the cuts over the next two years.

The council in Oxfordshire had been criticised by the prime minister’s own mother for its planned cuts to children’s services. On Tuesday night, Cameron’s aunt joined in the calls for the council to reverse its decision, saying it was a “great, great error” to allow 44 children’s centres to close. Clare Currie, sister of the prime minister’s mother, Mary Cameron, told ITV News that her nephew is a family man who she believes “doesn’t want them to be shut either”.

While Conservative county councils will get the most relief, allowing them to slow the pace of cuts, major Labour-run urban areas will get no transitional funding at all. Labour pointed out that the five most deprived councils in the country – Middlesbrough, Knowsley, Hull, Liverpool and Manchester – will receive nothing under the grant, while the five least deprived – Hart, Wokingham, Chiltern, Waverley, Elmbridge – will collectively receive £5.3m.

There have been growing warnings from Tory-run councils and Conservative MPs that they were not happy with the provisional settlement announced in December. The prime minister himself had urged Oxfordshire council to make cuts to back-office functions instead of essential services, which prompted a detailed riposte from his council leader, Ian Hudspeth, explaining the funding shortfall it would be facing.

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Tory councils in rural areas were expected to be particularly badly hit by reductions in central government grants between now and the end of the parliament, but Labour-run councils have borne the brunt of cuts so far since 2010.

Labour said the five most deprived councils have suffered an average £336 cut in spending power per person since 2010, compared with just £7 per person in the least deprived areas.

Essential services such as children’s centres, libraries, museums and elderly care facilities are under threat of closure in many parts of the country because of billions of pounds in extra cuts due this parliament. Their central government funding has already dropped by around 30% since 2010 and is set to fall by another 56% over the next five years, although some of this will be offset by other sources of revenue, such as the ability to keep business rates.

On Tuesday, librarians, authors and campaigners from across the UK descended on Westminster, protesting about closures and cuts to library funding by more than £180m over the last five years.

Steve Reed, Labour’s local government minister, said Cameron had engaged in a “blatant misuse of public money in a shameless attempt to buy votes and buy off Tory MPs”.

“The government is covering up where this money has come from and won’t explain why almost all of it is being handed to Tory councils just weeks before council elections across the country,” he said.

“Councils in poorer areas have suffered much harsher cuts since 2010 but they are getting next to nothing. The Tories have picked millions of pounds from taxpayers’ pockets to buy off their own MPs when faced with a rebellion in the run-up to local elections.”

A senior Tory source insisted the £300m of transitional funding applied proportionally across councils according to how much they were due to lose.

“Greg Clark has said there is a big rural funding gap, which we are addressing. This is a continuation of coalition policy,” he added.

A spokesman for the Department for Communities and Local Government said: “This long-term funding settlement for councils is fair, and ensures that councils facing the highest demand for services continue to receive more funding and have higher spending power than less deprived authorities. The transitional funding has gone to those councils facing the biggest fall in central government grant.”

“The settlement, for the first time allows councils to plan with certainty, with almost £200bn to spend on local services and a £3.5bn social care funding package over the lifetime of this parliament.”

The transitional relief fund is likely to persuade many of the Tory MPs who were planning to revolt to hold off for now. However, the Local Government Association said funding would still be challenging for councils over the next four years.

Gary Porter, chairman of the LGA, who was made a Conservative peer by Cameron last year, said it will go “towards easing the financial pressure on those local authorities who were adversely affected by the method of allocating funding and will ensure that no council will move into a negative grant funding position within the next three years”.

However, he added: “Funding reductions will still be challenging for councils over the next four years. Any extra cost pressures, such as those arising from rising demand or policies such as the national living wage, will have to be funded by councils finding savings from elsewhere.

“Many will have to make significant reductions to local services to plug funding gaps and will be asking residents to pay more council tax while possibly offering fewer services as a result.”

The Rural Services Network, which includes 150 councils in its membership, said that while it was pleased that the government had chosen to “smooth” the impact of the cuts, the move would not change the overall position over the next four years.