London’s poorest households have been hit by a £50m rent rise as housing associations quietly switch thousands of tenancies to higher rates to make up a shortfall in government funding.

About 11,000 homes in the capital have been converted from “social” housing to “affordable” since 2012, according to latest figures from the Greater London authority, and thousands more are to follow in a policy that has sparked tenants’ rebellions. Annual rents have risen by £29m, but the total cost to tenants over the three years to date has been £49.7m.

Social rents are typically half market rate, while so-called affordable tariffs are up to 80% of private rents, leading to complaints that the definition of affordable is Orwellian.

Many housing associations have exploited the category change to set rents at the highest possible level, with the effect that only relatively wealthy people can afford to live in homes originally meant for poorer tenants. Over half of the housing associations set the converted rents higher than 70% of market rate in the last recorded period in the City Hall figures. Others, determined to keep housing genuinely affordable, have charged much lower rents.

The system of changing the housing category when new tenants move in to a property means neighbours in identical flats can pay vastly different rents. The trend has accelerated since 2010, when the government made a 63% cut in capital investment budgets for housing associations, in effect a £3bn reduction in available funding.

“It is diabolical,” said Warren Levy, 70, a retired railway worker and chairman of the tenants’ association at Sutton Dwellings in Islington, owned by landlord Affinity Sutton. “My three-bed flat is £128.41 a week and they want to take that up to £300. They even asked if I wanted to move to one of their estates outside London, I presume so they could charge more for my place.”

Affinity said it had halted conversions at the estate after a protest by residents and said it would suggest tenants consider moving only if they had surplus room. In the past year it has converted 295 homes across its portfolio.

Among other associations, in the past three years, London and Quadrant switched 1,673 tenancies earning an extra £4.2m, Circle Housing switched 1,337 earning £3.8m more and Notting Hill Housing Trust switched 853 earning an extra £3.3m.

“These figures reveal what is happening across London: homes that should be genuinely affordable are not, when Londoners are desperate for rents to be lower,” said James Murray, executive director of housing at Islington council. “This change has been somewhat under the radar, but it is profound and very damaging for the future of the capital.”

The National Housing Federation (NHF), which represents housing associations, said its members were being forced to convert tenancies because of George Osborne’s deep cuts in investment budgets. The government has also demanded that any taxpayer investment in new housing should be in affordable rather than social rented homes.

“Our members are frustrated that they can’t build genuinely affordable homes as part of the government’s programme,” said Kathleen Kelly, assistant director of policy and research at the NHF. “Housing associations are now having to fund up to 85% of the cost of developing new homes from their own resources. They are not driving up rents because they want to, but are being forced to respond to the pressure on public spending.”

But a spokesman for the London mayor, Boris Johnson, said the policy of using the additional rents to build new houses had been a success.

“In 2011 the government identified the conversion of re-lets of existing social housing to ‘affordable rent’ as an important source of capacity in delivering the affordable homes that London needs. The mayor is on track to deliver his target of 100,000 low-cost homes over two terms, with 85,000 already completed.”

“The government and the mayor have been pushing housing associations to raise rents and ultimately this is a very political choice – and those responsible are the mayor and the government,” said Murray. “But some housing associations are putting the rents up more than others when they need to do more to keep rents down.”

Robert Kerse, finance director of Circle Housing, which has already converted 11% of its stock to affordable, said: “We would much rather the government continued to subsidise new affordable homes rather than raising rents, which is a future burden on the public purse through increased housing benefit costs, which could potentially outweigh the savings they are currently trying to make.”

He added that Circle tries to keep affordable rents below 60% of market rates, but said other social landlords had chosen to charge the full 80% allowed by the government.

Roger Harding, director of communications at Shelter, the housing charity, said the “so-called affordable rents are often way beyond the reach of many ordinary Londoners”.

“This is yet another example of London’s shrinking stock of genuinely affordable homes,” he said.

• This article was amended on 31 March 2015 and 1 April 2015. In an earlier version some figures were aggregated in error. The GLA has since said that its database was not presented clearly. Since the start of the 2012/13 financial year total extra rent charged has been £50m, not £70m. Annual rents have increased by £29m. The number of homes converted over that period is 11,000 not 25,000 . London and Quadrant converted 1,673 homes, earning £4.2m (not more than 3,000 and £7.4m). Circle Anglia converted 1,337, earning £3.8m extra (not almost 2,500 and £6.5m) and Notting Hill converted 853, earning £3.3m extra (not almost 2,000 and £6.4m). Affinity Sutton converted 295 homes (not nearly 1,000) over the past year.