A Conservative MP earning £74,000 a year says he has been forced to move back in with his parents because he can’t afford to buy a house.

William Wragg, 28, who earns three times the national average wage as MP for Hazel Grove, near Stockport, Greater Manchester, said he had become part of the so-called “boomerang generation” while he saves for a deposit.

This is despite self-contained one-bedroom flats being available in his constituency for rent at as little as £110 a week – just over an eighth of Wragg’s weekly take-home pay. He is also entitled to House of Commons expenses to cover the rent of a London flat.

Wragg told ITV’s The Granada Debate that although he was “paid extremely well” he had to move back home with his parents in the north-west or face being trapped in a rented flat.

“I am part of that ‘boomerang generation’ myself,” said Wragg. “In a few years hopefully I will have saved up enough for a deposit. I know exactly what it is like. I have complete empathy with people in that position. There is no getting away from the fact we face a severe challenge on housing in this country.”

David Hollingworth, a mortgage broker with London & Country, said that while there was no one-size-fits-all approach to mortgages, in general lenders could offer customers up to four times their salary, depending on their outgoings.

That would give Wragg a potential buying power of about £280,000, enough for a three- or four-bedroom family home in his constituency, once he has raised the £14,000 he would need for the minimum 5% deposit. Two-bedroom flats in Hazel Grove are on the market for as little as £110,000, which would require a deposit of £5,500.

Wragg gained a first-class degree in history from the University of Manchester and qualified as a primary schoolteacher in 2014 under the Teach First scheme to attract top graduates into teaching. However, until he was elected MP for Hazel Grove in 2015 he could only afford a rented flat. “When I think how much I spent on rent in a flat instead of a mortgage, I think maybe I made the wrong choice,” he said.

John Healey, the shadow housing minister, pointed out that as bad as things were for Wragg, they were far worse for many others. He said: “Since David Cameron took charge, home ownership has fallen every year, and now even Tory MPs claim they are paying the price.

“A generation of younger people are being locked out of home ownership, and even those with good incomes are now finding a place of their own is increasingly out of reach. If Mr Wragg thinks things are tough for him, he should spare a thought for the millions of aspiring homeowners earning far less than he is. I look forward to him joining Labour in holding ministers to account for their five years of failure on housing.”

Last October, research by building society Nationwide found that a fifth of young adults are staying in the family home until they are at least 26, with the same proportion of those not paying a penny towards their keep.

Young adults are being squeezed by low wages and rents that have hit record highs, while those who want to buy a property are finding the monthly cost of renting is preventing them saving enough to get on the housing ladder.

Research published at about the same time by the homeless charity Shelter showed half of tenants are spending so much on rent that they are unable to save towards a deposit, while a quarter could only put by £100 or less each month.

According to figures published by Shelter on Wednesday, an average young couple with a child would have to save for 12 years before they would be able to buy a home, while couples without children face a seven year wait.

Campbell Robb, Shelter chief executive, said: “Our drastic shortage of affordable homes is leaving young people and families across the country languishing in expensive and unstable renting, or living with their parents well into their thirties.

“The government has the chance to turn things around, but only if they commit to plans that can build homes that people on ordinary wages can actually afford to rent or buy.”

Dan Wilson Craw, policy manager for Generation Rent, which campaigns on behalf of private renters, said: “Moving back into the family home is the only way some young adults can save a deposit in today’s housing market. It’s an absurd sign of the government’s failure on housing that even one of its own MPs, earning three times the average, feels forced to do this. For ordinary renters without financial support, home ownership is a distant prospect.”