At least 350,000 households will be excluded from the housing market by 2020 because of a lack of affordable homes to rent or buy, according to a new report.

The figures, which were published as property website Rightmove reported the smallest November slowdown in asking prices in four years, underline how the rising cost of all private sector housing is locking out those on low and middle incomes.

Analysis by property firm Savills shows that, over the next five years, 70,000 new households a year will be unable to afford to rent or buy homes at a market rate unless assisted in some way. This means that 350,000 will need some form of housing priced at below market rate by 2020, the firm said.

The figures use current incomes and prices for buying and renting and assume a household can pay up to 30% of its gross income on housing. They do not include “any backlog of unmet need and the effect of falling stock levels due to right to buy and proposed sale of high-value council homes,” Savills said, which suggests the impact of rising prices could be even more severe.

The problem is, unsurprisingly, most acute in London and south-east England, where property prices have leapt up and are above the peaks reached before the financial crisis. Savills said 26,000 new households in London and 11,500 in the south-east were set to be priced out each year. It said that while the median income of excluded households in the capital was £20,000, those earning as much as £60,000 a year would not be able to afford housing costs in some parts of the city.

On Thursday, official figures showed that the number of new homes created in England increased by 25% in 2014-15, although there was a rise in the number of properties sold off through right to buy. Government schemes to allow builders to avoid affordable housing quotas on developments that include starter homes or involve a change of use could mean further struggles for priced-out buyers.

Chris Buckle, associate director at Savills research, said: “There can be no question that we need to boost housebuilding volumes, but these new homes need to be built across a variety of tenures to put homes within reach of those in greatest need.

”Our concern is that new policy will result in a greater shift from sub-market rental products towards more expensive shared ownership and starter homes accessible only to those on middle incomes.”

Figures from Rightmove show the traditional winter dip in asking prices is less pronounced than usual, suggesting sellers are not in a rush to move.

The average asking price for properties coming on to the market in November was 1.3% lower than that for new sellers in October, against an average drop of 1.9% over the past five years. The average asking price across England and Wales is now £292,572, still 6.2% up on the same month in 2014.

Rightmove’s housing market analyst, Miles Shipside, said: “Those looking to market their property as Christmas gets closer often have a greater sense of urgency to find a buyer and sensibly recognise that trimming their asking price will provide an incentive to potential buyers more focused on seasonal Christmas trimmings.

“Buoyant market conditions and a confident outlook for 2016 mean that the reduction, while no doubt welcome to hard-pressed buyers, is the most Scrooge-like since 2011. It’s likely to be a shortlived respite as the combination of high confidence and low interest rates is a recipe for higher prices next year.”

The website said a survey of 23,000 homeowners revealed that people were feeling confident about their finances in 2016. The majority (85%) said they did not think their financial situation would worsen in the next year, despite the possibility of an interest rate rise. Just over two-thirds predicted that property would continue to rise in price over the next 12 months, with only 7% expecting prices to be lower.