A Tory planning minister has admitted that the coalition's new wave of garden cities would not have to contain a single affordable home, despite Nick Clegg's claims that they would offer low-cost accommodation and help solve the UK's housing crisis.

As the government unveiled plans for new garden cities containing 15,000 homes each, it emerged that developers would not need to reserve a certain proportion of the properties for those struggling most with the cost of living.

Asked by Labour whether the first garden city in Ebbsfleet would contain low-cost homes, Nick Boles, a Conservative minister, said the government would "not impose a particular level of affordable housing for housing schemes".

"Unrealistic Section 106 agreements [which specify how many affordable homes should be built] result in no development, no regeneration and no community benefits," he added.

Under changes brought in by the coalition, developers can challenge requirements for affordable housing imposed by councils, with some firms arguing that they depress the prices they can get for properties in the rest of the development.

Clegg said a new wave of garden cities would "provide affordable homes, good schools, and jobs for the next generation, whilst at the same time preserving the countryside" as he invited communities to bid for funding from a £2.4bn pot to host the new developments by 2020.

However, the prospectus launched by the government only said that local areas "may wish to consider" mixed-tenure homes which were "affordable for ordinary people". It added: "The government does not wish to impose any definition of what garden cities are, but instead intends to work with localities to support them in developing and delivering their own vision."

Clegg said he hoped that a new set of cities would help create an "ark of prosperity" in the south-east, where people wanted to live but were currently unable to find houses.

Labour accused the government of failing to tackle the housing crisis early enough and of ignoring the issue of whether any new homes would actually help those struggling to find affordable accommodation.

Roberta Blackman-Woods, a shadow communities and local government minister, said: "The government is failing to tackle the housing crisis and as a result, home ownership remains out of reach for too many low and middle-income earners. It is vital that the government takes affordable housing seriously in any plans for new development, but so far they have avoided such a commitment. We would expect that any proposals brought forward for new garden cities to address the growing need for affordable housing."

A spokesman for the Department for Communities and Local Government confirmed there were no Whitehall targets for the number of affordable homes in garden cities.