At 5.55am, Talgarth Road, one of the major arteries into west London, is just beginning to clog up with early rush-hour traffic. A man named Dave, his white van pulled over into a loading bay, is putting up a billboard poster by the side of the carriageway. The previous one was an advert for Calvin Klein featuring the model Lara Stone. Over the course of 20 minutes, Dave covers Stone up, expertly pasting rectangles of paper over her, using a ladder for the high ones, then sweeping over with his brush.

The first rectangle, in the top left corner, contains a headshot of Jacob Rees-Mogg and the beginning of his Twitter handle. As Dave lines up edges, pastes and brushes, and Stone disappears, a quote emerges from Rees-Mogg. This one wasn’t a tweet; he said it in parliament. “We could have two referendums. As it happens, it might make more sense to have a second referendum after the renegotiation is completed.”

There are three other men here, dressed in hoodies, lumberjack shirts and beanies, lurking around and admiring the work. Their work – because Richard, Adam and Chris are three of the four key people behind Led By Donkeys, the remainer guerrilla activists highlighting the hypocrisy and lies of politicians by posting their damning quotes on billboards around the country. Less guerrilla now, actually: they’ve gone legit, this hoarding is paid for. Before, they just took them over. The reason it is going up so early is because that’s when Dave operates, mainly for parking reasons. Still, Richard, Adam and Chris are not their real names; they don’t want to be identified.

When Dave – which as far as I know is his real name, he’s just been employed for the job – is done and has gone, we retreat from the frontline to a nearby Costa, for coffee and pastries, to warm up and for Richard, Adam and Chris to explain themselves. Long-time friends, they work at management level for NGOs and charities. United by a WhatsApp group, by politics, a dislike for Brexit and a need to do something, they also all have young families, children aged between one and seven. It is hard to combine direct action with feeds, drop-offs, homework and bedtime. Their partners are understanding and supportive, they say. They live in London and Bristol. The fourth member lives in Europe, outside the UK, with his non-British partner and kids.

Boris Johnson’s ‘great deal’ quote on a billboard in Leeds. Photograph: Steve Morgan

This is just about boys having a laugh, isn’t it, or the beginnings of a midlife crisis? “I think there is a midlife crisis but it’s on the part of the nation, not on the part of us as individuals,” says Richard. “Britain is having a post-imperialism mid-, possibly late-life crisis where it’s not quite sure what it’s doing. It’s just gone and bought a motorbike and a leather jacket, it’s a midlife crisis called Brexit, and I don’t think it’s going to work out.”

Richard, 44, talks the most, but knows it, and stops to allows the others in. Adam, 43, is quiet and measured, but steely, and the bravest when it comes to climbing ladders. Philosophical Chris, 39, the baby of the group, is not unmodel-like himself, and wouldn’t look out of place on a billboard. Chris came up with their name, after the first world war phrase about soldiers – lions – being led to their deaths because of the appalling decisions of British generals. “Often we [the British] have a reputation for being boringly sensible and yet here we are in this unreal moment of chaos and masochism and nobody really knows why we’re doing it,” he says. “We’re putting up quotes of these donkeys, these leaders, who are leading us off this precipice, highlighting what brought us to this point. It seemed to make sense.”

It all began, as most good ideas do, in the pub. They were talking about the infamous David Cameron tweet – “Britain faces a simple and inescapable choice – stability and strong government with me or chaos with Ed Miliband” – which was doing the rounds again after Theresa May cancelled the vote on her deal in December. And someone said: why don’t they slap it on a billboard, make it the tweet you can’t delete?

The next day, on the WhatsApp group, one of them said they had found someone who would print it out for them. They all agreed: “Let’s just fucking do it.”

John Redwood’s tweet, Leeds. Photograph: Steve Morgan

It was cheaper to do five, so they cobbled together four more tweets – from Michael Gove, David Davies, John Redwood and Liam Fox – not really thinking they’d ever put them up. Initial outlay was about 200 quid, plus £90 on a ladder from B&Q.

There are no how-to-put-up-a-billboard tutorials on YouTube. The nearest they found was a timelapse video by a man promoting his own poster business. There was a delay on the first night because Richard’s daughter wouldn’t go to sleep, but eventually, one evening in January, they found themselves by the A10 in north London, Adam up the ladder covered in wallpaper paste, bits of paper flapping all over the place, Cameron’s face wrapped around his own head … Finally, after an hour and a half, it was up.

That first one was on top of an ad for Halifax. So they stole the space? “We temporarily borrowed advertising real estate from a company that could afford to lend it to us,” Richard clarifies. “We didn’t necessarily ask permission but it was public service and therefore totally justified.” They would later borrow from Ford and McDonald’s, too.

And it felt good. “There is the thing about taking it out of the digital zone,” says Adam. “The actual tangible visceral nature of having these things up on the street and having these guys held to account really works, I think. When we saw that we had that moment of: hold on, this is a thing, it could work.”

They got to the pub for last orders (dry January went out of the window). The next morning they tweeted it, someone picked it up and retweeted it, they had 1,000 followers, the Guardian’s Marina Hyde retweeted it, they had 2,000, then 3,000 (now they have 43.6k).

Dominic Raab’s quote, Birmingham. Photograph: Led By Donkeys

There is no point preaching to the converted, though; they knew they had to get out of London and into leave areas. Sunderland would have been hard when you’ve got kids that wake up at 4.30am, not to mention day jobs. But they took Michael Gove to Romford. And then there was Dover, which felt right because of its central place in the drama, with Dominic Raab producing choice quotes. “That fucker was going up in Dover even if we got nicked,” says Richard, who holds a special place in his whatever the opposite of heart is (spleen?) for Raab.

They talk about Dover the way a band might talk about their breakthrough gig. It was the night of the meaningful vote. They drove down after work in Adam’s Toyota, listening to it all on 5 Live, the lobby bell and everything, with (new) rolls and paste and hi-vis in the back, and the ladder on the roof. They had identified four sites on Google Street View, but when they got there, one of them, on the side of an MOT centre, looked too high. Not for Adam, though: up he went, with Liam Fox’s “the easiest trade deal in history …” There were barking dogs, sudden floodlights, encounters with pissheads. “Just own it,” said Richard, meaning look the part, and they did.

Richard, Adam and Chris did four in Dover that night. As well as Fox, there was Theresa May, “the Emperor Donkey herself”, with “Remaining a member of the European Union means we will be more secure from crime and terrorism”; Rees-Mogg’s second referendum endorsement; and Raab’s, of course: “I didn’t quite understand the full extent of this but … we are particularly reliant on the Dover-Calais crossing.”

They were done at 2am and drove home. It had been brilliant fun, but they had reached a point where they couldn’t carry on doing this as well as being good dads and partners. Also, they had spent about 500 quid of their own money. So the next day they set up a Crowdfunder.

They reached their initial target of £10,000 within three hours, and soon they were up to £50,000. “We were like: ‘Oh shit’,” says Chris. “With this comes responsibility.”

A Leave.EU quote, Bristol. Photograph: Led By Donkeys

There was, says Richard, the danger they would end up with millions in the bank “and absolutely no knowledge or wherewithal to spend it. So we did what you never do on Crowdfunder, which is to say stop sending money until we know what to do with it.”

What it did mean is that they could now pay for people who knew how to put up billboards to put them up properly, and in places they wouldn’t have been able to reach. Billboards that would stay up, for two weeks or a month, rather than getting ripped down the next day. As in the film Three Billboards Outside Ebbing, Missouri, their campaign had hit a nerve. People were sending in their fivers and tenners.

Not everyone wanted to help. The biggest owners of advertising sites wouldn’t have them, too political (though they were happy to host Ukip). But they found smaller companies with fewer sites who were more accommodating. At the moment they’ve got 30 up, with another 60-plus booked in. They’re all over Britain and they would like more; they’ve got the money for it.

They have been shocked and touched by the response. Not just the money, but the messages and support. Once it was a bunch of friends, with a baby in the middle of the night, maybe, searching for what they could find on Iain Duncan Smith or whoever, on Twitter or Google or the They Work For You function of Hansard. Now the crowd is sourcing quotes.

A lot of people like them feel frustrated and powerless, “the idea we’re shifting towards this precipice and nobody is actually going, ‘Hang on, why is this happening?’” says Chris. “When this tiny little idea came out, it was something practical and tangible we can do. It’s that cathartic element of feeling like we’re doing something, and the messages we get from people echo that.”

A Michael Gove quote, Rochdale. Photograph: Led By Donkeys

Adam agrees. “Doing something that is real and out on the streets has really resonated with people.”

“We’re not so arrogant as to think that four dads with a ladder are going to turn this thing around,” says Richard. “But a heist was committed in 2016 and it feels like standing outside the bank watching the getaway car screaming into the middle distance with no one tracking them down. OK, it’s two and a half years late, but we are chasing these people down.”

“If it makes it even a little bit harder for these guys to come out with the same bullshit lies because they know they’re going to get called out on it, that’s an achievement,” adds Chris. “Introducing that tiny amount of accountability into our politics is something I would have loved to have been a part of.”

Adam, who does a lot of international work, says he knows of people in other countries who want to use the billboards device. It’s a tactic that can be used whenever and wherever. Which reminds them, they do have actual day jobs to go to. Hang on, quickly – now what? Well, they’ve got other ideas, such as one to get closer to some of the people saying this stuff, but they won’t say more than that. And they are certainly not going to stop with the billboards, what with all the momentum they’ve got, money in the bank and the quotes that just keep on coming.

Don’t put that ladder away Dave … oh, Dave’s left. And he is a leaver, he admitted quietly earlier. Well, he didn’t actually get round to voting, but he would’ve voted leave if he had. He’s happy to do this, though: it’s just a job.

• This article was amended on 7 February 2019. An earlier version referred to one of the billboard team living “in Europe with his European partner”. This has been clarified to “in Europe, outside the UK, with his non-British partner”.