Freedom of information requests submitted by the housing and homelessness charity revealed that 55% of those living in temporary accommodation, or 33,000 families, were employed.

The number of working homeless has nearly doubled from 19,000 when Shelter last looked at the figures in 2013.

The charity blamed the 73% increase on high private-sector rents, the ongoing freeze in housing benefit, unstable tenancies and the shortage of social housing.

Shelter’s chief executive, Polly Neate, said: “It’s disgraceful that even when families are working every hour they can, they’re still forced to live through the grim reality of homelessness.

“In many cases, these are parents who work all day or night before returning to a cramped hostel or B&B where their whole family is forced to share a room. A room with no space for normal family life like cooking, playing or doing homework.”

She added: “We cannot allow struggling families to slip through the cracks created by our housing crisis - the government must urgently come up with a new plan for social housing that delivers the genuinely affordable homes we desperately need.”

The highest proportion of homeless working households in temporary housing was in London (60%); followed by the east of England (44%); and the south-east (44%). The lowest was Yorkshire and the Humber (9%). The north-east is the only region where the proportion of working homeless has decreased since 2013.

The biggest increases in homeless working families between 2013 and 2017 were seen in the east Midlands (167%); the north-west (89%); and the West Midlands (46%), reflecting the growth of the housing crisis beyond traditional high-rent areas such as London.

A ministry of housing, communities and local government spokesperson said: “Everyone deserves a safe and decent place to live and we are providing more than £1.2bn so all those left homeless get the support they need.

“Councils have a duty to provide suitable temporary accommodation to those who need it, and families with children get priority. So families can get a permanent home, we are investing £9bn in affordable properties, including £2bn for social rent housing.”

A Channel 4 Dispatches documentary will explore the issue on Monday night.