Those of us with only a smattering of knowledge about the ancient world know one thing about Cato the Elder. During Rome’s long wars against Hannibal, Cato ended every speech in the senate with the same words: “Carthage must be destroyed.”

“Brexit must be stopped” is unlikely to last as long as Cato’s catchphrase has managed to. But it focuses the mind. Those who think Brexit must be stopped are not the majority. But they have a case and a cause, and they are right. So how might stoppage be achieved?

Probably not by a political movement headed by Tony Blair. The former prime minister is not heading back into frontline politics. But he is one of the biggest names to insist that Brexit is not yet irrevocable. He told the New Statesman last week that Brexit “can be stopped if the British people decide that, having seen what it means, the pain-gain cost-benefit analysis doesn’t stack up”. And on that he is absolutely right.

When inflation rises and growth slows next year, make sure Brexit’s role is clearly spelled out

Blair carries so much baggage that it is inconceivable he either could or should play the leading role in any campaign. The Iraq war was wrong and it is no part of my argument that the past can be brushed aside. But Blair has serious things to say about Brexit that serious people ought to listen to. It’s time his critics were big enough to give him a break. The 439-70 House of Commons vote this week against the SNP’s effort to sanction Blair for the events of 2003 may suggest there is some space for the former Labour leader to at least be heard. But don’t hold your breath.

If Brexit is to be stopped it will require time, a change of public mood, and an alliance. The SNP, Greens, Liberal Democrats, significant parts of the Labour party and a minority of Tories would all have roles to play. People from outside politics are crucial too. This week’s joint press conference by Nick Clegg, Chuka Umunna and Anna Soubry was a start. But as Clegg says, to turn the referendum around needs the people’s consent, not a procedural trick. This will only happen if the public mood changes. Anti-Brexit campaigners should try to change it, and here’s how.

The first point is to be clear who they need to be talking to, rather than squabbling about which of them is entitled to do the talking. The name of this game is changing minds. So there is absolutely no point crafting a campaign that is aimed at fundamentalist Eurosceptics who never wanted Britain to be part of the EU in the first place. Nor is there any point in focusing on racists and xenophobes. People who don’t like foreigners or people with coloured skin are not going to change their minds.

But that leaves a lot of people who voted for Brexit, in hundreds of thousands of cases, on the basis of their own experience. They were sold a false prospectus by the leave campaign; but they need a better one, which offers them hope, support, material improvements in their lives, and confidence. Theresa May gets this, though she is doomed to promote Brexit and not to stop it. Those who want to stop Brexit need to learn this lesson: the aim of any campaign must be to persuade these voters that there is a better way of getting the things they want than leaving the EU. Don’t berate, persuade. And get out of the bubble.

The second key principle is to accept that this is a long game. Brexit won in June 2016. It won’t be turned around quickly. Stopping Brexit is on the margins of political possibility right now. It could be that Brexit will be slowed by the supreme court’s ruling, due in January. But that’s just the start. Opponents of Brexit should settle in. Time is on their side.

The negotiations with the EU will take a minimum of two years – longer if there is a transitional phase. The pressure to bring things to a head will be enormous and will grow, both in Britain and in the other 27 EU countries. British opponents of Brexit must be EU reformers too.

The third point is to remember Cato. Chip away, every day. Every time something new and troubling happens, make it clear that things would be different if Brexit were stopped. This week’s immigration figures showed a pre-referendum surge. Without Brexit this wouldn’t have happened. Hate crimes have proliferated. Brexit shares the blame for that. When inflation rises and growth slows next year, make sure Brexit’s role is spelled out. If ministers abandon the single market in favour of migration curbs, make Brexit’s responsibility clear. Unless anti-Brexit campaigners have established in the public mind that there is a clear and viable no-Brexit alternative, they won’t be in a position to make the most of their opportunities.

The fourth point is the other side of the same coin. The leave campaign lied through its teeth about the benefits of Brexit. It said there would be £350m extra every week for the NHS. Last week the chancellor said precisely nothing about any extra NHS spending in the next four years. And look what is actually happening to the NHS. The leave campaign landed the May government with a huge promise that it cannot deliver. The opposition parties need to link the two at every opportunity.

Stopping Brexit will not be easy. Recovering from a big defeat is hard. The campaign is more likely to fail than to succeed. The Brexiteers will fight very dirty. But the prize is immense – and Hannibal was not defeated in a day.