There are only 43 potentially suitable homes in London currently available that would be “affordable” for the typical young family buying their first property, according to research by Shelter.

The charity says that in 35 local authorities there are no appropriate homes available for first-time buyers at all, mostly in the south-east and London. They include Cambridge, where Shelter estimates the most expensive home a young family on average incomes could afford would be £125,684.

Looking at listings of properties with two or more bedrooms on the website Zoopla, the housing charity found that just 0.1% of those in the capital would fall into what they defined as an “affordability threshold”.

This threshold was calculated using an estimate of the average earnings of families in the area and the amount they could borrow based on that income, according to data released by the Council of Mortgage Lenders.

This results in the price of an affordable home varying across the country. The housing charity puts it at £184,597 for families in Richmond upon Thames compared with £110,724 in the east London borough of Newham.

In total, Shelter found 42,185 two-bedroom homes across England that were affordable to young families – fewer than one in five listed on Zoopla.

The north-east of England was the region with the most affordable homes for families and 42.2% of properties listed there fit into that bracket.

In every single local authority in the north-east, at least one in ten of the homes is affordable for those on a median income. This is not true of a single local authority in London.

Mansfield in Nottinghamshire was the locality with the least expensive affordable family home at £100,169.

Shelter defines its typical young family as aged between 23 and 29 with one or two children, with one part-time and full-time earner.

It was assumed that they had saved a 17% deposit and could get a mortgage of 3.4 times their income. According to the latest Annual Survey of Hours and Earnings, the median income for a family of this type is £30,748.

Young couples with no children, for whom the median income in England is £43,446, would fare much better in the market. They would find 32.3% of the properties listed on Zoopla affordable. However, a single first-time buyer, typically earning £21,851, would only be able to purchase 7.5% of those same homes.

Properties with zero bedrooms, those with shared ownership and those referencing retirement were taken out of the analysis.

The latest figures from the English Housing Survey showed that home ownership in the country had fallen to its lowest rate in nearly three decades, with 63% of households defined as owner-occupiers.

Roughly one in five households in England were rented privately in 2013-14. However, this is much more extreme in London where renters are in the majority.

Campbell Robb, chief executive of Shelter, said: “For the next government, whoever that may be, it’s time for the talk to stop and the work to begin. Politicians need to act swiftly to deliver the plan that will build the 250,000 homes we need.”

Although the research was based on homes listed on Zoopla, Shelter said its work was in no way endorsed by the property website. They also admit there are some limitations to the dataset – for example, if houseboats and a mobile home had not been included in the London figures then the proportion of affordable properties would be even lower.