Austerity cuts have fallen hardest on deprived communities in the north of England, which are enduring the highest poverty rates and weakest economies, according to a study.

The Centre for Cities thinktank study shows that the poorest areas have borne the brunt of council spending cuts. Local authority spending has fallen nationally by half since 2010, with areas such as Liverpool, Blackburn and Barnsley facing average cuts twice that of their counterparts in the more affluent south, according to the thinktank.

The report suggests there is a “city and country” divide, with urban council areas having shouldered cuts to services such as street cleaning, road repairs and libraries, which, are, on average, twice as deep as those borne by leafier authorities.

The Centre for Cities said the Treasury review of public spending due this autumn must find extra funding for all councils, and for urban areas in particular, if authorities are to remain sustainable in the face of soaring demand for social care.

Andrew Carter, the chief executive of Centre for Cities, said: “Councils have managed as best they can but the continued singling out of local government for cuts cannot continue. Fairer funding must mean more funding for cities.”

Councils’ traditional role as “custodians of places” is under threat as a result of the cuts, according to the thinktank. Some councils are at risk of becoming “little more than social care providers”, as they reduce non-care services to the bare legal minimum to pay for rocketing demand for services for vulnerable adults and children.

Nearly half of cities spend at least half of their overall budget on social care alone, up from 38% of budget in 2010. The biggest increases in social care spending have been in deprived cities outside the south-east of England. In Barnsley, 62% of the entire council budget went on social care in 2017-18.

The report comes as controversy grows over ministerial proposals to redraw the funding formula for local government, which critics say would transfer scarce funding from the poorest inner-city neighbourhoods to affluent Tory-controlled county areas.

The report states: “Despite the high-profile coverage of the struggles of county councils in recent years (most notably Northamptonshire), it is actually cities, and especially those in the north of England, that have been hit hardest by austerity.”

The five cities and towns that have suffered the biggest falls in spending over the past eight years are from the north of England: Barnsley (-40%), Liverpool (-32%), Doncaster (-31%), Wakefield (-30%) and Blackburn (-27%). The British average is -14.3%.

Liverpool residents have borne the largest spending cuts per head on local services of £816 over the period. The city has lost £441m in annual spending. Barnsley has had £145m cut from its annual budget, which is equivalent to £688 a year per head.

London has seen the biggest absolute cuts, with £3.9bn stripped from spending on services by its 32 boroughs since 2009-10. The Centre for Cities says the capital has shouldered 30% of all local government cuts in Britain, despite having just 16% of the population.

British cities, which are home to 55% of the population, have borne 74% of the total cuts to local government spending since 2009-10. In per-head terms, this equates to a cut of £386 in urban areas, compared to a £172 reduction in the rest of Britain.

Deprived northern urban areas have been traditionally more reliant on government grants than more affluent councils because their relative poverty means they are less able raise cash though local taxation to pay for higher social needs. Ministers have targeted cuts on central grants, disproportionately hitting poorer councils.

Increasingly, councils are turning to commercial investments to patch up holes in their budgets, the report says. Billions have been borrowed to invest in office blocks, shopping centres and even airports and shipping companies. Although this raised £1.2bn last year for English local authorities, it covered just 5% of the income lost to cuts.

Councils are also balancing the books by charging residents for services such as parking, recycling and social care. York city council has increased its income from charges more than any other city over the past eight years, the report says. A quarter of all spending comes from this source.

The Liverpool mayor, Joe Anderson, called for an urgent review of the fairness of local authority funding. The city would be £80m a year better off if it had endured cuts at the national average, he said. “The government is turning a blind eye to the reality of what is happening to local authorities, in particular, the poorest.”

Councillor Richard Watts, the LGA Labour Group finance spokesperson, said the targeting of the least well-off parts of the country for cuts had contributed to many of these “left behind” areas voting leave in the EU referendum. “Government should be supporting communities that are crying out for investment, rather than starving them of vital resources,” he said.

The Tory-controlled County Councils Network (CCN) said its members faced a £3.2bn budget shortfall by 2020 and called for increased spending in all authorities. “We endorse Centre for Cities’ call for an end to councils’ austerity,” said Simon Edwards, CCN’s director.

The communities secretary, James Brokenshire, said: “We are investing in Britain’s future by providing local authorities with £91.5bn over the next two years to meet the needs of their residents. This coming year, local government is getting £1bn extra in funding – a real-terms increase – to strengthen services and support local communities.”

“On top of this, we are delivering on our vision for a strong Northern Powerhouse economy with wide-ranging support including a historic £13bn investment to improve journeys for commuters and motorists and over £5bn for devolution and growth deals.