Button worked as a carer and shared a two-bedroom home with a long-term partner. When she died suddenly, he lost the house, and within weeks he found himself shifting a rotting badger’s carcass to make room for his tent on the outskirts of the Wiltshire town. He cooked food over an open fire with a boot scraper improvised for a grill. He quickly learned of the hostility homeless people can face. He came back one day to find his tent and possessions, including a picture of his late partner, burnt to ashes, apparently on purpose.

The prosperous town, 10 miles from Bath, is in a county that claims to have only 22 rough sleepers, down from 33 last year. These figures will be sent to central government and used to help determine homelessness policy, but they may well underestimate the scale of the problem. In London and Manchester tents fill shop doorways, but in the countryside the homeless are elusive, sleeping, like Button, in woods, or in vans, bin sheds and on river banks. They are hard to count.

Wiltshire, like other councils, tallies its rough sleepers once a year. The latest snapshot was taken last month and in Chippenham they found three. Since May, Chippenham’s homeless hostel, Unity House, said it had looked after 46 at-risk or current rough sleepers.

The county trumpeted its figures as evidence it was getting on top of the problem. Richard Clewer, a cabinet member for housing, said it was “such good news”. But people in Chippenham who have been living the cold, fitful, anxious life of the rough sleeper were sceptical.

A £100m government drive will aim to end rough sleeping in England by 2027. The new strategy, being launched by James Brokenshire, the communities secretary, on Monday, will offer help with mental health and addictions, as well as targeted support to get rough sleepers off the streets and into long-term accommodation.

Brokenshire acknowledged that efforts to tackle homelessness had “not been good enough” and said he wanted to see quick progress in reducing the estimated 4,751 people sleeping rough on any given night in England.

He told the Sunday Times the growing number of people sleeping on the streets was not consistent with “the type of country, the type of society that I profoundly believe we are”.

Brokenshire said: “To see that number of people on the streets isn’t good enough. We need to make progress quickly with the new strategy.

“We shouldn’t punish people for being homeless. This strategy is about how we can support people, how we can direct, and yes, sometimes challenge, some of those who are living rough to get into those services that will help make a difference.”

The new strategy will take a three-pronged approach of prevention, intervention and recovery. About £30m will be spent on mental health and treatment for the misuse of substances, including the synthetic cannabinoid spice.