The Bleak Houses report by children's commissioner for England Anne Longfield said there are 124,000 children who are officially homeless and a further 90,000 forced to "sofa surf".
Official figures related to homeless families are also called into question. Longfield says that they are failing to capture the number of parents who are deemed to have made themselves "intentionally homeless" and those who are unable to claim benefits due to their immigration status.
The report warns that a further 375,000 children are living in households in rent or mortgage arrears, putting them at risk of homelessness in the future.
The increasing use of shipping containers as temporary homes for families is a particular concern to Longfield. These units typically have only one to two bedrooms, are subject to overcrowding and are too hot in the summer months, while being too cold in winter.
"One mother told us she had to sleep with the front door wide open and that her baby got heat rash - but are too cold in the winter," states the report.
"They are often not properly designed with children in mind. Ovens and other dangers can be too close to the ground so that they are in reach of very young children."
Office blocks and warehouses are also being used increasingly to create flats to house homeless families with children. These flats are often cramped, as little as 18 square metres in size, adds the report.
Longfield is also concerned about the length of time families are forced to live in temporary accommodation. Her research shows that in 2017, around 51,000 children have been in temporary accommodation for at least six months. About 6,000 have been in such temporary housing for at least a year.
Of the 2,420 families known to be in bed and breakfast housing in December 2018, a third had been there for more than six weeks.
"Something has gone very wrong with our housing system when children are growing up in B&Bs, shipping containers and old office blocks," said Longfield.
"Children have told us of the disruptive and, at times, frightening impact this can have on their lives. It is a scandal that a country as prosperous as ours is leaving tens of thousands of families in temporary accommodation for long periods of time, or to sofa surf.
"It is essential that the government invests properly in a major house-building programme and that it sets itself a formal target to reduce the number of children in temporary accommodation."
Commenting on the figures, Just for Kids Law chief executive Enver Solomon said: "Every child has the right to a safe and secure place to call home, but every day we are approached by children and their families who are facing homelessness or housed in temporary accommodation that is not fit for purpose.
"This puts children at serious risk, affecting their development, contributing to mental health issues and damaging their life chances.
"As cuts to benefits and local authority budgets leads to rising demand for dwindling services, all too often we see local authorities practice an insidious form of gatekeeping to avoid providing children and their families with the support they are entitled."
He added: "The government must take a serious look at the findings of this report and act urgently to ensure the funding and infrastructure are in place to ensure that all children are provided with the safe and appropriate housing they need to develop into healthy adults."