The milkman of human kindness is angry. Not just generally, but specifically now, as he arrives at a BBC building in central London. On the train up from Dorset, where he lives, Billy Bragg has read about British soldiers in Kabul firing shots at a poster of Jeremy Corbyn.

He is angry because it is, he says, symptomatic of the demonisation of politicians, particularly on the left, particularly Corbyn, and because of what it says about the rising threat and reach of the far right. He is also angry because of the timing of it: the news comes the day Corbyn is going to sit down with the prime minister, the day after headlines about a plot by a neo-Nazi to murder a Labour MP.

And he is angry because he has had a Twitter ding-dong with someone who said it was just squaddie banter and that Bragg should “chill the fuck out”. No, said Bragg, he would not. “Can you not see how this brings shame on everyone who serves? I did a bit of time myself and have always had respect for those who wear the uniform, but this trashes their reputation,” he tweeted back.

We take the lift up to the third floor, to BBC Radio 6 Music, into the corner office of the station head, Paul Rodgers, who is out. When we finish, he’s waiting outside, happy to have had his workspace taken over by Billy Bragg. Bragg is not just an angry leftie but also a musical legend, don’t forget. Essex poet, folk singer, songwriter, punk and romantic, as well as political activist, his songs have outlasted many of the ideas and some of the people he’s railed against for 40 years.

We are supposed to be talking about Bragg’s new skiffle documentary, which we will get to, but it is hard to think about anything except the state of the country at the moment. Clearly the Labour leader shouldn’t be used as target practice, but isn’t Bragg disappointed in him?

No, he says. He broadly supports what Corbyn and the Labour party are currently doing. “There are things I don’t agree with, but he represents something really important, which is the rejection of the neoliberal agenda,” he says.

It goes back to before Corbyn’s leadership, to the 2010 general election that no one won, Bragg says. No majority means governments, of whatever flavour, can’t do whatever they want. Since then, there have been a series of moments when the public has defied Westminster and the way they do things, he believes.

“You’ve got to see the election of Corbyn as part of that. We all know the circumstances in which he was nominated. For him to have won suggests it’s not about him – it’s about those of us who voted for him, and what we would like to see. Corbyn isn’t an event, he’s a process.”

Corbyn and Bragg at Glastonbury 2017. Photograph: REX/Shutterstock

Whatever he is, what about him going awol for much of the Brexit mess, not providing any serious opposition to this shattered shambles of a government? Not guilty, says Bragg. No other party has tried to appeal to both remainers and leavers, or striven for consensus rather than taking sides, as Corbyn has.

“He is constantly underestimated. I wouldn’t be surprised if we look back on this and find that the ambiguity that everyone criticises him for is seen to be the best thing he could have done. I think it would have been a trap for him to go for another referendum, because that would have had the effect of uniting the Tories and also rallying Ukip.”

Has he played a blinder, then? “No, I never said that. But sometimes you play a game and you don’t have the rub of the green but you eventually win.” Translating it into football terms (Bragg, originally from Barking, east London, supports West Ham), we settle for the recent game between Liverpool and Spurs as the best analogy. (Liverpool won with a lucky, late own-goal.)

Failing to root out antisemitism is an issue, Bragg concedes. Is Corbyn antisemitic? “I don’t think so. No,” he says. “I think there is a problem. The party has a problem, the leadership has a problem – and the problem is they have not taken it seriously from the start.”

I remind Bragg of another Twitter spat he had last July, in which he seemed to be saying that the Jewish community has “work to do” in order to rebuild trust with Labour. He holds up his hands and says he messed up. “I failed to recognise the right of the Jewish community to decide for themselves what does and doesn’t constitute racism. It’s the Macpherson principle, and I made a very insensitive response to someone’s question that implied that I knew better than the Jewish community about what is and isn’t. I personally don’t believe it amounted to antisemitism, it was just very insensitive. It denied them the right to decide what is a racist attack on their community, and that’s wrong and I apologise for it.” It would be nice to see politicians do that more often: admit when they got something wrong.

What about the skiffle? Coming, but first briefly back to Brexit. Bragg isn’t calling for a second referendum, because it would polarise the debate again. “It depends if you want to reverse Brexit or resolve it,” he says. “I don’t want to be talking about this for the rest of my 60s, and I’m only 61. I’d like it to be resolved, and in order for it to be resolved we need to find a consensus about it rather than another winner-takes-all referendum.”

So he would like to see a citizens’ assembly, which has been called for by Gordon Brown among others, that would allow people to talk about why they voted the way they did, and come to some sort of agreement about what to do next. “It may be that a citizens’ assembly would recommend another referendum, but at least we would have come to it through a consensus rather than a kneejerk reaction.”

He was on the London People’s Vote march last month, though (try keeping Billy Bragg away from a protest). And he was struck by the flags. Lots of European ones, union jacks, Welsh flags and Scottish flags, but no English ones, probably because people wouldn’t have felt comfortable with them.

“Don’t tell me there weren’t any English people there: the majority were English. The absence [of flags] has something to do with what we’re trying to deal with because Brexit is an English phenomenon and an English nationalist phenomenon.”

Is his progressive patriotism more difficult in this climate? “More necessary. I love my country and I don’t want it to make an absolute fool of itself on the world stage, as it currently is. Until we allow ourselves to be comfortable with what we are, English, then I think the far right are always going to have a hold of it.”

Skiffle band and dancers in Soho Square, London, in the 1950s. Photograph: Hulton Deutsch/Corbis via Getty Images

There are a few other good manifestations of Englishness, apart from flags, he admits. “Our national sporting teams, the men’s football team, the women’s football team. Look at other nations, they’re not so multicultural as us, maybe the French, not the Germans. Getting to the semis of the World Cup last year, that’s who we are. Raheem Sterling standing up against racism, that’s who we are, that’s what it means to be English.Raheem is a really good example of it. We need more of that – we need to recognise ourselves.”

The English don’t even have a national anthem, he says. Could it be one of his? A New England? “I don’t want to change the world, I’m just looking for a new England,” he sang on his 1983 hit. “No, not New England. The worst thing you could do to a song is make it a national anthem. It would be like Things Can Only Get Better – don’t even go there,” he says, shuddering at the memory of New Labour. “It would have to be Jerusalem, wouldn’t it?”

Aside from politics, Bragg still loves writing songs and performing them. He is currently touring One Step Forward Two Steps Back, already in the US and soon Britain, where he does three nights in a venue, the first of which includes newer stuff, then a couple of retrospective ones. It allows him to stay a bit longer in a city rather than constantly moving on. If you wanted to hear The Milkman of Human Kindness, say, you’d go on the second night. I love that song. “So do I,” he says.

Music has maybe lost some of its vanguard role in youth culture, he says. “Everything you wanted to say about the world, there was only one medium. Music told you how to dress, who to like, who to hate, where to go, where not to go. Obviously, social media has that role now. Music has lost its central place where everyone gathered, so it’s bound to be now more about entertainment. But young people still struggle to make sense of their lives. There are a number of ways you can channel that, and music remains one of them.”

Though he doesn’t claim to be totally up to speed on it, Bragg recognises that grime is where the energy is now. The punk of today, the skiffle. Skiffle! We haven’t even got to it and there’s a knock at the door – time’s just about up. He wrote a book about it in 2017, Roots, Radicals and Rockers, and now he’s done a BBC documentary that tells the story of Rock Island Line, originally an African American prison work song from Alabama, and how it came via New Orleans and trad jazz to London and Liverpool and Lonnie Donegan. Crucially, it was open to anyone else who could play three chords on a guitar, or a washboard, or a tea-chest bass. And so was born a youth movement that shook up Britain in the late 1950s, leading to pop, rock and punk – and everything that followed.

Bragg at the launch of Red Wedge, an initiative to get young people interested in politics, in 1985. Photograph: Rex/Richard Young

It is an important social story, as well as a significant musical one. “The thing about skiffle is that it’s really the first manifestation of culture made by teens for teens in our history, so in that sense, it really does deserve more credibility than it has,” Bragg says.

It’s all there, in the film. But Brexit has eaten into our skiffle time, as it does with everything.

“The schism of Brexit goes right through the layers, and will ultimately destroy everything it touches,” he says, getting up from the head of 6 Music’s leather sofa. “It will destroy the Conservative party; it could destroy the Labour party. But having said that, the UK is long due political realignment, and I think this is part of the process.”

His hope is that the experience will help inoculate us against populism. “We will look back into the chasm of it, and realise how fragile our social contract is – as a community, as a nation – and make a promise not to go down that path.”

Now he’s going back to Dorset, where he lives with his partner, Juliet Wills, who manages him, in a big house on a cliff looking out to sea, which has led to accusations of champagne socialism. This doesn’t bother him.

“Me and my missus have worked hard over the years, and the result of that is we have a really nice house. It’s all our own – neither of us inherited any money. I’m very fortunate they pay me to do the things I’ve always wanted to do.”

Sometimes he goes to Waitrose, sometime Morrisons. “It depends what I want. After years of stringent testing, I’ve found out that the hummus is better in Morrisons.”

We walk to the tube together. He tells me about walking along the clifftop at home, which he does with Nordic sticks – you know, ski poles. It gives him a bit of upper-body exercise, gets the heartrate up a bit. And he tells me how to make a skiffle bass, using a tea-chest with a hole cut in it, an old broom handle and a length of baler twine.

“Try and get a bit about skiffle in it, will you,” he says, disappearing into a tunnel.

Rock Island Line: The Song That Made Britain Rock, BBC Four, 12 April, 9pm. Tour: billybragg.co.uk/giglistings/