Millions of people are facing unaffordable rents, long waits for social housing, or are priced out of the market when they are ready to buy.
The average house price in England was £300,000 last year – almost eight times average earnings.
The Labour government has pledged to build 1.5 million new homes in England over the course of this Parliament – but it is already falling behind on this target.
Andy Burnham is credited by some people with overseeing a building boom in Manchester as mayor of the Greater Manchester Combined Authority, although critics say there remain serious housing problems in the city region.
BBC Verify has looked at the scale of the housing challenge facing Burnham once he becomes PM, and examined whether there is anything we can learn from his record as mayor to see how he might tackle it.