King’s Cross station at 10.30 p.m. is not a happy place. Most commuters have long returned to their centrally heated homes, leaving the concourse free for the homeless to roam randomly in search of a few coins from stragglers.

I was there to catch a late train to Potters Bar last week and almost missed my Cambridge--bound service due to the numerous men and women who approached and asked for money. Some looked dishevelled, disturbed, miserable; others were polite and seemed resigned to rejection. I keep thinking about one man in particular. He said he was an ex-soldier — a ‘veteran of conflict’, as he put it — and that he had not eaten all day. It was chilly but he was wearing shorts and had a soiled blanket over his shoulders.

I said, piously, that I gave to charity in a number of ways and that in any event I did not have any spare change. I am not certain that the bit about spare change was true. ‘Hear me out,’ the man kept saying as I headed for the barriers by platform 9. But I chose not to do so.

What’s going on at King’s Cross reminds me of arriving in New York in the early 1980s to work as an intern on a newspaper. I was shocked that so many doorways and entrances to shops, especially around Times Square, had become dormitories for the homeless.

The situation in the rest of London and in every major city in the country is now no different. But it seems especially poignant in King’s Cross because that part of town is held up as a paradigm of successful regeneration after developers moved in and the prostitutes and sex shops moved out.

The newly opened Coal Drops Yard, a plush mall with some 50 designer outlets and restaurants, opened a few weeks ago; Google has offices in the area and Granary Square is where a trendy crowd drink cocktails on the banks of the Regent’s Canal.

The latest figures on people sleeping rough in England — rather than the overall statistic on homelessness, which includes those in temporary shelters and hostels — show that on a given night in October last year, 4,751 people were sleeping on pavements or in doorways, or, as the Ministry of Housing puts it, other ‘places not designed for habitation’. That’s a 15 per cent increase on the previous year and more than double the number in 2010. Nearly a quarter of those 4,751 people were sleeping rough in London. The total number of homeless people in the UK, in all its various definitions, is officially around 240,000.

No one pretends that these figures are wholly accurate (the charity Crisis thinks the real numbers could be almost double), but in any case it seems almost inconceivable that Theresa May will fulfil her pledge to halve rough sleeping by 2022 and eliminate it altogether by 2027. The word ‘homelessness’ didn’t even feature in the Chancellor’s budget speech, although removing the borrowing cap on local authorities for house-building might make a difference.

No one likes to see homeless people on the streets and we need to find a political solution, but it’s the politics that always gets in the way. The left wades in with its weary refrain about ‘heartless Tory cuts’ while the right mounts its high horse and talks about encouraging a ‘dependency culture’, whereas most people accept that it’s a complex issue involving mental health, drug and alcohol addiction, family breakdown, migration and a whole range of other factors.

And that’s before you start on the toxic combination of a lack of new housing for first-time buyers, low wages, ‘no-fault evictions’ by landlords and welfare cuts as a result of the freeze in Local Housing Allowance.

‘As it stands, the government is investing over £1 billion a year on temporary accommodation — which means we are spending vast sums to maintain the problem rather than solve it,’ says Jon Sparkes, chief executive of Crisis. Or as Polly Neate, chief executive of Shelter, puts it: ‘You can’t end homelessness without homes.’

That’s where Housing First comes in, a project launched two years ago that has its roots in the US but is currently operating as a £28 million combined authority pilot scheme in Greater Manchester, the Liverpool City region and the West Midlands. Rather than spending vast sums preparing people for running their own homes, the scheme seeks to house people immediately and then supports them in taking responsibility for whatever their needs might be, whether medical, social or financial. If you have your own front door, it gives you the stability to progress and helps build self-esteem. This might sound dangerously optimistic but it has achieved positive results in a number of countries, both big and small.

In the US, a four-year study in 2006 reported that the retention rate for those in the Housing First system was 88 per cent compared with 47 per cent in ‘treatment first’ models. And in Finland, where it was introduced in 2007 by a centre-right government, it has effectively ended homelessness altogether.

The main challenge for Housing First is finding suitable accommodation. That means persuading councils to free up existing social housing or convert shelters into self-contained units. For it to be successful, the private sector must also buy into the project; and although landlords might be reluctant to rent to those wholly dependent on housing benefits, they would at least know their tenants were long-term and were the recipients of intensive support.

Despite the Prime Minister’s promise, homelessness is hardly a top government priority and certainly not a vote winner. Yet it shouts at us every day as we walk along any major street in any major city and makes us feel horribly uncomfortable.

And so it should, because according to PwC, rolling out Housing First over the next decade would cost £9.9 billion but would deliver benefits worth £26.4 billion in terms of reducing costs to the NHS, the prison service, local authorities and, ultimately, would lead to an increase in tax contributions. That means that for every £1 invested, an estimated benefit of £2.70 would be generated.

If I were the chancellor that would make sense; but, then again, if I were the chancellor in a government with a wafer-thin majority I might just do what previous incumbents in the job have done — and shove the issue in a bottom drawer.