In 83 local authority areas which accounts for over a quarter of the country fewer than one in 10 homes were affordable, assuming the family could save the typical deposit for a first-time buyer.
For those hoping to buy with smaller deposits the situation is even worse with 88% of homes for sale in England unaffordable for families with a 95% loan.
In Cambridge there were only three affordable homes for sale while in Brighton and Hove there was one.
In 14 local authority areas including Ealing, Lewisham and Slough, there were no affordable homes being sold at all.
Campbell Robb, chief executive of Shelter, said: “When a family looking to buy their first home searches a whole town for a place to live and finds nothing they can afford, it's clear we’re not just facing a housing shortage any more, it’s a full-blown drought.”
The shortage is countrywide, as in Exeter eight out of 553 homes on the market were affordable while in South Lakeland in the North West just 4% of the 1,069 properties for sale were cheap enough.
Single people have the least chance of getting on the housing ladder, as only seven out of every 100 homes on the market can be afforded by someone on the average wage.
Even couples without children, who have two full-time incomes are likely to struggle. In a quarter of the country, fewer than ten out of every 100 homes for sale were affordable for a childless couple on average wages.
Campbell Robb added: “Our failure to build more homes is leaving a whole generation of young people with no choice but to remain trapped in expensive and unstable private renting, or stuck in their childhood bedrooms for years to come, no matter how hard they work or save.
“What we need right now is for politicians to roll up their sleeves and make stable homes for the next generation a top priority.”
On Shelter’s website consumers can enter their postcode to discover how many affordable homes there are in their area.
ONS statistics recently revealed that UK house prices have climbed by 9.9% in a year to average £260,000.
Homeownership in England has now fallen to its lowest level since 1987.
