Local opponents have described the supermarket’s proposal that just 27 of the 683 homes in the Ilford project will be available for affordable rent as “insulting”.

Planning experts for the mayor of London, Sadiq Khan, have said the offer “falls substantially short” of City Hall’s plan to deliver 17,000 affordable homes per year – equivalent to 40% of the strategic housebuilding target.

It also falls well short of the London Borough of Redbridge’s target of 50% affordable housing across all new developments. There are currently over 8,000 households on the waiting list for affordable housing in the area, and more than 2,400 living in temporary accommodation.

The borough estimates it needs an extra 15,000 affordable homes by 2033. The case is set to go before a public inquiry starting on Tuesday, but the project appears likely to go ahead after the council withdrew its opposition on Saturday.

Sainsbury’s says the “maximum reasonable” amount of affordable housing it can include is 14 one- and two-bedroom flats, a dozen three-bedroom units and a single four-bedroom property. It estimates making a 20% profit selling off the private flats, according to planning documents. At current local prices that could exceed £40m.

It has described it as “a financially challenging project”, partly because of lost revenues to its retail operation when it closes its existing store for construction. It has also agreed to pay Redbridge £11.4m in community infrastructure levy, although this cannot be used to fund affordable housing.

But Meenakshi Sharma, co-founder of Ilford NOISE, a local residents group, said the amount of affordable housing being offered was “ridiculous and insulting”.

“People can’t believe it is 4% especially with all the publicity about the need for affordable housing,” she said. “And yet this still carries on. They don’t take any notice whatsoever. There’s a big housing need in the area. There are lots of people in temporary accommodation and lots of overcrowding.”

It is the latest in a series of high-profile battles over the financial viability of private housing schemes in the capital with councils seeking to maximise the number of cheaper homes in developments and developers seeking to minimise them. Previous disputes have centred on central London sites where developers have argued that the high cost of land limits their ability to subsidise affordable housing, but the row over the Ilford site suggests the issue is spreading to the outer London suburbs.

Affordable in this case means rents capped at 60% of market rates. Sainsbury’s is increasingly moving into housebuilding, using the space above its stores for housing. The Ilford project is its largest yet, but it has also built 650 homes around a store in Nine Elms and 500 homes above a store in Fulham, both in London.

Redbridge had originally rejected the application because of the lack of affordable housing and was planning to oppose it at the public inquiry, but it has now reversed its position and accepted the 4% offer.

On Friday, a spokeswoman for Redbridge told the Guardian: “We declined the application because of the huge gap between the borough’s expectations on affordable housing in new developments, and the proposals we were given. The capital is critically short of housing, especially affordable housing and we need to increase the stock in the borough.”

But on Saturday it told the planning inspector it was withdrawing its opposition and would not resist Sainsbury’s appeal against its original refusal.

In a letter to the planning inspectorate, the head of planning, Joanne Woodward, said it had agreed common ground on the financial viability of the project and a planning deal, although without any increase in the affordable housing included in the development.

“The council will attend on the first day of the inquiry to explain how the position it has now adopted has been reached,” she said.