Boris Johnson is set to approve plans for “affordable” flats that the Guardian understands could cost tenants up to £2,800 a month to rent.

The London mayor is expected to grant consent on Friday for the construction of 98 “affordable rent” apartments on the site of the Royal Mail’s Mount Pleasant sorting office in central London in a deal that critics say makes a mockery of the idea that affordable housing is for the most needy.

Confidential estimates of market rents filed as part of the application suggest tenants could be charged up to £1,170 a month for a one-bedroom flat and up to £1,690 for a two-bedroom flat. A family occupying a four-bedroom flat in the development could be asked to pay as much as £660 a week. According to a rule of thumb widely used by housing experts that housing costs should represent a third of income to be considered affordable, their family income would need to be around £100,000.

Sarah Hayward, the leader of the London borough of Camden, said the expected rents on the Mount Pleasant scheme were among the highest ever seen for affordable housing.

“If these rent levels are as claimed, they will not be in any way affordable,” the Labour councillor said. “Boris Johnson is showing his true colours. He doesn’t want poor people living in London.”

The homes represent less than a quarter of those being built as part of the 681-unit development on the prime site that straddles the border of Islington and Camden and could be worth as much as £1bn. The boroughs have objected strongly to the lack of cheaper units and believe the project would remain commercially viable if 50% of the homes were genuinely affordable.

The rents the Royal Mail Group (RMG) calculates the homes would attract if placed on the open market are contained in a confidential financial appraisal submitted to the mayor’s office based on figures provided by the property consultancy Knight Frank. A separate draft legal agreement says the “affordable” units will cost no more than 60% of market rents in the area and will on average have a discount of 44%.

“This is not affordable at all to most people who need it … [Boris Johnson] has perverted the definition of ‘affordable’ and made a mockery of the whole idea that affordable housing is there to help the people who need it most,” said James Murray, the executive member for housing on Islington council.

“Rent on a one-bed council flat close to this development is no more than £175 a week and people struggle with that. The idea you could add another £100 and it still be affordable is ridiculous. It shows Boris Johnson either doesn’t understand social housing in London or doesn’t care. This development is set to deprive Londoners of genuinely affordable housing while benefiting investors in luxury flats and Royal Mail shares.”

The mayor’s office said it was satisfied that “the price per square foot for the affordable housing is reasonable and that a reasonable forecast of sales, rents and costs is set out” in documents provided by the Royal Mail and its consultants.

“Providing more affordable homes, both to rent and buy, is one of the mayor’s top priorities, and the report to be considered by the mayor proposes to double the amount of affordable housing in these planning applications,” Sir Edward Lister, the deputy mayor for planning, said.

“The mayor is on track to build a record 100,000 low cost affordable homes for Londoners over his two terms, with more than 77,000 already completed. This year alone, more affordable homes are being built than in any other year since 1980. Methods for calculating how affordable rent levels are set are specified in national policy and we would expect the final figures to reflect that guidance.”

Johnson decided in January to call the scheme in and use the mayor’s power to decide on the application. The move followed local criticism that the proposal was “fortress-like”. In June he said it would be “a wonderful place to live”, sparking complaints from Emily Thornberry, the local MP, that he could not be considered an impartial judge.

The housing charity Shelter said the decision to peg “affordable” rents to market rents has made them unaffordable.

“Examples like this illustrate how the people in most urgent need of genuinely affordable housing are being squeezed by soaring property prices in London and a new definition of affordable rent that is not affordable in real terms for many people,” said Toby Lloyd, Shelter’s head of policy.

Tom Copley, the London assembly member who leads on housing for Labour, said too little of the site was being used for affordable homes.

“This is a site that was until recently owned by the taxpayer, which is now being developed for big profits for RMG shareholders,” he said. “The taxpayer has already lost once due to the undervaluation of Royal Mail when it was sold. Now they’re losing again.”