An estimated 280,000 homeless people will be rough sleeping, or living in temporary housing and hostels in England on Christmas Day – about one in every 200 of the total population, according to Shelter.

The housing charity’s figure, which is likely to understate the true level of homelessness because it does not count people who are sofa-surfing or living in sheds or tents, is 3,600 higher than in 2018, and up 23,000 since 2017.

London continues to be the centre of homelessness, accounting for 170,000 of the total England figure. One in every 52 people in the capital are homeless, with the borough of Newham, where one in 24 are homeless, being worst hit.

Some of the other highest rates of homelessness were in Birmingham (where one in 66 residents are homeless), Manchester (one in 102), Brighton (one in 75) and Luton (one in 46), reflecting the growth of the problem outside the capital.

While the homelessness growth figures for London have remained relatively stable in the past two years (up 4%), the problem has exploded in north-west England (up 117%), the West Midlands (up 64%) and the East Midlands (up 50%).

Polly Neate, Shelter’s chief executive, said: “As well as those facing serious ill health or even death sleeping rough on our streets this winter, there are thousands of families trapped in grotty emergency B&Bs, with no space for children to sit and eat, let alone play. This is the grim truth our new government must confront and do something radical to change.”

Across Britain, at least 135,000 children will be homeless and living in temporary accommodation on Christmas Day – the highest number for 12 years, Shelter estimated.

Charities say rising homelessness is being driven by a lack of affordable housing and the failure of housing benefit – which has been frozen since 2016 – to keep pace with spiralling private rents. Private tenants on benefits face an average £113 a month shortfall between their local housing allowance and their rent.

The Shelter figures comprised people in temporary accommodation, rough sleepers, people accepted by councils as homeless who have yet to be allocated a home, single people in hostels not counted as formally homeless, and families living in homes arranged by social services under the Children’s Act.

Previous years’ estimates have included Wales and Scotland. These showed a Great Britain total of 307,000 homeless in 2017 and 320,000 in 2018. Wales and Scotland were excluded in 2019 because of changes in the way they collect homelessness data.

Boris Johnson placed tackling homelessness on his “huge agenda of delivering social justice” in remarks to his cabinet on Tuesday. Officially, recorded homelessness has risen by 39% over the past decade of Conservative rule.

A spokesman for the Ministry of Housing, Communities and Local Government said: “We’re giving £1.2bn to tackle all types of homelessness. Everyone should have somewhere safe to live, and councils have a duty to provide accommodation to those who need it, including families with children.”