More than half of families housed in temporary accommodation after being accepted as homeless by their local council are in work, according to the housing charity Shelter.

The number of working homeless has nearly doubled since Shelter last looked at the figures in 2013. There are now about 33,000 “working homeless” – or 55% of all households in temporary accommodation – compared with 19,000 in 2013, it estimates.

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.”

Working households were typically turning to their council for help after losing a tenancy and finding themselves priced out of their local area by soaring rents.

The loss of a private-sector tenancy is the biggest single cause of homelessness in England, according to Shelter, accounting for more than a quarter of all homelessness acceptances.

The shortage of suitable affordable homes meant homeless households were often placed in cheap hotels, hostels, or large houses with a family in each bedroom, Shelter said.

It cited the case of Mary Smith, 47, who lives in temporary accommodation in Watford with her three sons, but works full-time in a shoe shop.

Mary Smith, who works full-time in a shoe shop, said she and her sons became homeless after being evicted by their landlord. Photograph: Benjamin Youd/Shelter/PA

She said they became homeless after being evicted by their landlord and could not afford to rent privately. “I nearly lost my job when I first became homeless because the transport links from my hostel were so bad.

“We’ve lived in three different temporary places in two years, and it’s been really tough on the children. We don’t want a palace, we just want a place that we can call home.”

The phenomenon of working families – including nurses, taxi drivers, council workers and hospitality staff – finding themselves homeless was highlighted by the local government ombudsman last year.

Michael King said the common perception that homelessness was about people with chaotic lives who slept rough no longer held true: “Increasingly, [homeless people] are normal families who would not have expected to be in this situation.”

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.

Since 2010, the overall number of homeless people in temporary accommodation in England has grown by 61%. Council spending on this form of housing reached £845m in 2016. Last year a cross-party group of MPs said homelessness in England was a “national crisis”.

Shelter used freedom of information requests to analyse official government data on temporary housing, benefits and employment as well as conducting a tenant survey.

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.”