In a wide-ranging interview, Prime Minister David Cameron applauds our Homeless Veterans campaign and tells Evening Standard owner Evgeny Lebedev that relations with Vladimir Putin can be mended

‘The Prime Minister will be down in a few minutes,” said the charming housekeeper, “once he’s finished taking exercise.”

Of all the men (and one distinguished woman) for whom Chequers has been a country retreat since 1921, few were as devoted to fitness as the present one, who runs regularly and makes extensive use of the gym here.

When David Cameron comes downstairs five minutes later to meet me in his wood-panelled study, wearing a navy-blue suit, open-neck white shirt with blue checks, polished black shoes, and with flushed cheeks, he is slightly out of breath. Ordering black coffee — I ask for the same — he wonders aloud when he and I last met.

I was invited to his residence in the rolling Chilterns to discuss this newspaper’s Homeless Veterans appeal, which has been an extraordinary success. Together with its sister papers, The Independent, Independent on Sunday, and i, we have raised more than £700,000 for the brave men and women who serve our country overseas but fall on hard times when they return to civilian life. Or rather, you have raised it, because it is above all thanks to the generosity of you, our readers — a point Cameron makes  several times himself.

All prime ministers are effusive about the armed forces — partly, no doubt, because they hope some of the heroism and splendour will rub off on them, within voters’ line of vision. But over the course of an hour, it becomes clear to me that Cameron’s respect for our servicemen and women is deep.

“I think we have an enormous duty to those who serve us,” he says, after offering warm congratulations on our success. “Obviously many veterans find their place in life afterwards and get on with life. But some tragically do fall through the net and suffer from problems of mental health and other issues, and it’s to them that we owe the greatest debt of all.”

I had asked him to outline what,  specifically, the coalition Government had done to improve the lot of veterans. Cameron appointed Lord Ashcroft, a donor to our campaign, to review the support veterans receive upon their return.

Mr Cameron and Evgeny Lebedev at Chequers, his official country residence  

The list of changes made is impressive: he mentions redirecting funds from the Libor scandal in the City toward veterans; putting the military covenant into law; and the new military covenant committee in Whitehall, which meets monthly.

“There’s a whole list of things,” he says, “from the pupil premium [going to veterans’ families] to dealing with inquests better, to scholarships for those who lost mums and dads in action, to council house discounts, to better rights to healthcare.”

This commitment, he says, is partly a result of his 13 visits to Afghanistan, and of the fact that RAF Brize Norton is in his constituency. But won’t the coming cuts to expenditure across all government departments, which the Institute for Fiscal Studies describes as “colossal”, jeopardise all this? “No it won’t, because we’ve made sure the Ministry of Defence isn’t just the Ministry of Defence, but also the Ministry for Veterans and their families. In terms of the defence budget, we’ve said that we’re going to keep increasing its size.”

Perhaps so; but aren’t the stories uncovered by this newspaper, of veterans enduring extreme hardship, shocking? And why should it be up to readers to provide for them? “First of all,” he says, “full credit to your campaign because I know it has raised awareness of a very important issue, and I know it has brought forward funding from, for instance, the Mayor of London... The truth is there’s always been a role for veterans’ charities.”

Such as, of course, the two that this campaign has supported: Veterans Aid and ABF The Soldiers’ Charity. I suggest that the outpouring of respect for our military, not least during commemorations of the Great War last year, with all those poppies at the Tower of London, has been deeply humbling.

Evening Standard proprietor Evgeny Lebedev speaks with David Cameron at Chequers  

“I think that we revere our military because they represent the best of British — the values they live by, the courage, service above self, teamwork, patriotic belief in service,” he says.

Turning to the general election, on the morning of our meeting the airwaves are thick with the latest polls, giving Labour a stubborn lead over the Tories.

Given his party may need to win by a few percentage points if it wants the parliamentary majority to which he has long aspired, but is yet to achieve, where will the late surge come from?

At this point he mentions several themes familiar to anyone who follows Westminster. The choice, he says, is one between competence and chaos, the latter being the inevitable result, in his view, of a government led by Ed Miliband. Voters have to be told to stick to the plan. “The only [poll] that counts is on election day.”

The Government’s economic record speaks for itself, he says. At a recent meeting of the European Council, for instance, he noticed Britain had created more jobs in the past four years than the other 27 countries seated around the table put together. But if this record is so impressive, why is his party behind? What does he think is the most important thing he has yet to explain to the British public?

“Look, people had a very tough time in this country. We had a recession where people lost jobs, [with] pay cuts and pay freezes. People sometimes had the number of hours they could work cut, or frozen. And it takes time to recover from that.

“The central question for the Government was, can you get Britain on a more secure path... You need time to demonstrate that that will benefit everybody.”

I figure that readers of this newspaper will hear more than enough about this stuff between now and May 7, so change the subject to one close to my heart. War rages in eastern Ukraine. Last week’s ceasefire agreement in Minsk is tentative to say the least. Lady Thatcher once said Mikhail Gorbachev was a man she could do business with. Would he say the same about Vladimir Putin today?

“Well he’s someone I have a relationship with and can talk to and we’ve had very robust discussions about Ukraine as we have about Syria and other things. Of course these things can change, but they will require a change of approach.” Separately, he is clear that “Islamist fundamentalism is the greatest threat we face”.

The instability, Cameron says, is  primarily Russia’s fault. Can relations be mended with Putin in the Kremlin? “Yes, they can...but border insecurity in Europe is the last thing the world needs. I actually think it’s the last thing that Russia needs, but the answer lies in his own hands.”

I tell him I agree, but it’s suddenly clear that our time is up, and a visiting dignitary has already been kept waiting longer than is polite. He poses for photographs, says goodbye, and prepares for his next guest.

As we head out along the curving approach road, and back toward London, my abiding impression is of a leader on a treadmill in every sense, enjoying the privileges of power, conscious that it won’t last forever, and grateful to readers of this paper for their support on a cause dear to his heart — and mine.