Councils in inner London are set to become the biggest losers under a government plan to update council funding rules, a think tank says.

The Institute for Fiscal Studies (IFS) found some London boroughs could see their funding levels drop up to 12% once inflation is taken into account.

But areas in outer London are set to gain from the changes, the researchers found, along with urban areas outside the capital including Nottingham, Wolverhampton and Slough.

The government argues the overhaul is necessary because councils’ funding has become out of step with local demand for services.

The new funding system, to be phased in over three years from 2026, will see changes to the formulas used by government to capture levels of demand for council-run services, along with the differing cost of delivering them.

A greater share of funding will be redirected towards areas with a higher share of properties in lower council tax bands, whilst the portion of business rates income that councils have been allowed to keep since 2013 will be redistributed.

The IFS predicts the proposed changes are set to redistribute around £2.1bn in annual government funding, with 186 authorities losing out and 161 benefiting.

It will not be possible to say exactly what the changes will mean for each area until the plans are finalised later this year.

But the think tank said Camden, Hammersmith and Fulham, Kensington and Chelsea, Wandsworth and Westminster would see their overall funding drop by 11–12%, even accounting for a proposed funding floor to limit losses.

These areas are set to lose out under the government’s proposed method to even out differences in council tax revenues, given they have low rates and many properties in higher bands, it added.

Outside London, the East Midlands and Yorkshire and the Humber regions are set to see the biggest increases in funding, according to the report.

Areas with relatively high – but not the highest – population densities are also set to fare well, it estimates, including outer London boroughs and councils in Blackpool, Nottingham and Slough.

It added that the widest range of outcomes would be seen in shire district councils, where some councils where business rate income has grown most, such as Mid Suffolk and North West Leicestershire, would lose out.

Other such districts in more urban areas, such as Harlow, Crawley and Norwich, are among the biggest winners.

The share of funding going to the very poorest areas will be substantially larger, it added, than for the least deprived.

The shake-up will affect the share of central government funding distributed to councils in England, including income they are allowed to keep from business rates.

This currently represents around half of their income, with councils raising the rest locally, subject to a 5% cap on yearly increases.

Funding is allocated according to a complex mix of formulas taking into account factors like population and deprivation.

Labour ministers argue the current rules, which have not been updated in over a decade, are failing to reflect higher demand for council services in poorer areas.

The Liberal Democrats said the changes would “come as a shock to the system for many councils,” branding the changes “robbing Peter to pay Paul”.

“The government is moving the pain of chronic council underfunding from one community to another instead of delivering the economic growth that would deliver the revenue to fund local services everywhere,” added deputy leader Daisy Cooper.

A spokesperson for the local government department said: “The current, outdated way in which local authorities are funded means the link between funding and need for services has broken down, leaving communities left behind.

“That’s why we are taking decisive action to reform the funding system so we can get councils back on their feet and improve public services”.

Although there is widespread agreement among councils that the current system is badly in need of updating, designing a new one poses a political headache for ministers ahead of a significant set of local elections due next year.

Many local leaders have warned that current funding levels do not cover the rising cost of mandatory services such as adult social care and special educational needs, despite real-terms funding increases in more recent years.