A reallocation of council funding could redirect hundreds of millions of pounds from so-called left-behind communities in the north of England to the leafy southern shires, analysis has found, leaving many newly Conservative voting “red wall” areas facing fresh cuts to local services.

Under a review of the local authority funding formula, £320m a year could be shifted out of councils in England’s most deprived areas while Tory-controlled shire councils mainly in the south-east gain £300m.

High-profile losers include many constituencies that elected new Tory MPs in December, including Workington, which would suffer from Cumbria county council’s £5m loss, and Sedgefield, which would feel the impact of £10m being taken out of Durham county council.

An estimated 37 of the 50 new Tory MPs – amounting to 70% of the gains made by the Conservatives at the general election – represent areas that are set to lose millions a year. Other notable losers include Stoke-on-Trent, Redcar, West Bromwich, Bishop Auckland, Grimsby and Leigh.

The analysis, commissioned by the Local Government Association, presentsBoris Johnson with an early test of his promise to “level up” resources between the south and the north and Midlands. The government is expected to issue a formal consultation on the new formula, which has been developed over the past 12 months, in the spring.

The LGA’s Labour group said Hampshire would be the biggest winner, gaining £35m a year, followed by Surrey county council (£25m), which is home to 11 Conservative MPs including the cabinet members Dominic Raab and Michael Gove. Big losers include Birmingham, which would lose more than £48m.

The Tory-run Northamptonshire county council, which declared effective bankruptcy in 2018 after years of financial mismanagement and is still in special measures, is set to get a £7.5m boost to its budget. At the time, ministers have refused to bail it out, saying this would be a reward for failure.

The Conservative-run East Sussex, council, which hit the headlines in 2018 after warning that cuts would pare local services back to a “bare legal minimum”, stands to gain £6m a year, while Wokingham in Berkshire, one of England’s most affluent boroughs, could get a 30% funding rise.

Johnson made a high-profile visit to Sedgefield – for many years Tony Blair’s seat – the morning after the election to celebrate his party’s emphatic victory, and he promised to repay the trust of voters who had helped propel him to power by switching from Labour to Tory.

The shadow communities secretary, Andrew Gwynne, said: “In the new parliament, 37 Tory MPs represent communities at the sharp end of these cuts. They know these changes are wrong, so it’s time for them to decide: what comes first, their communities or their careers?”

The analysis models the likely differential effect on councils’ adult social care funding allocations from 2021 using a proposed new government methodology used to direct funds to local authorities. Labour says officials have privately confirmed that the figures are sound.

The Conservative-controlled LGA said the analysis was a “high-level indication of the broad direction of travel” rather a precise guide to the impact on individual councils. It said additional funding was needed to ensure no council loses out financially.

An LGA spokesperson said: “This analysis does not represent LGA policy, an LGA policy proposal or an LGA preference. It is an attempt to provide some information to councils that might help gauge the likely impact of the fair funding review on the relative distribution of adult social care funding.”

A decade of austerity has disproportionately targeted deprived areas of the north and Midlands. English councils have lost on average more than a third of their government funding since 2010, triggering cuts across a range of local services.

The proposed methodology comes out of a fair funding review announced more than a year ago under Theresa May. It was seen as the outcome of heavy lobbying by Tory shires, which have argued they are unfairly allocated less money per head of population than inner-city areas.

Labour councils have previously criticised the fair funding review for removing deprivation as a factor in the allocation of cash, adversely affecting urban areas. The LGA analysis is the first time the impact on individual councils has been robustly modelled.

Failure to reverse the direction of travel implied in the methodology could prove personally embarrassing for Johnson. His Uxbridge constituency in the London borough of Hillingdon would get a £8.8m funding boost under the new system.

Nick Forbes, the leader of the LGA Labour group, said: “After 10 years of Tory rule, the social care crisis has got worse and worse and worse. These changes will force further cuts and further hardship, and once again the most vulnerable in society will lose out.”

When finalised, the proposed formula will also adjust the allocations in other areas of council spending including general funding, public health, children’s services and roads. Labour predicts there will be further cash transfers from north to south in these categories.

A government spokesperson said: “Funding allocations for adult social care should be fair and based on the best available evidence. We will continue to progress the fair funding review through close collaboration and engagement with the local government sector, and aim to publish a consultation with indicative allocations in spring 2020. Councils should continue to use official government data for their financial planning.”

This week an independent study found that the average low-income family in the deprived “red wall” areas won by the Tories would lose income under universal credit, the government’s £60bn-a-year reform of the benefit system.

• This article was amended on 25 January 2020. Universal credit is a £60bn-a-year scheme, not £60m as stated in an earlier version.