To get a real understanding of the implications of a no-deal Brexit for the majority of the UK, I spoke over the weekend to the chairman of one of the country’s biggest and best-known supermarket chains. Supermarkets are the great levellers: we may not all own a car, or care about bankers having passporting rights, or visit other European countries for our holidays, but we certainly all step inside one supermarket or another in our day-to-day lives. It seemed like a good place to start, even if what I found out was distinctly unsettling.

The supermarket chairman – who I will keep anonymous – started the conversation by reminding me that the EU provides 30 per cent of what his supermarket sells in food and groceries. If we were to leave the European Union and trade on WTO rules, his supermarket is working on the basis that tariffs will be levied on goods being imported to the UK from the EU. So, for example, cheese will attract a 44 per cent tariff, beef a 40 per cent tariff, lamb a 40 per cent tariff, chicken a 22 per cent tariff, apples a 15 per cent tariff and grapes a 20 per cent tariff, and so on.

Not all of the costs of the increased tariffs would be passed directly onto the consumer but, he said, “we will roughly see a 10 per cent rise in food prices and the impact on fresh food will be particularly disastrous because it is more expensive to bring it in from the rest of the world than from the EU”.

Those who he expects to suffer most are customers on low incomes: “The British consumer will have a big cut to their standard of living, particularly for people at the bottom of the income scale, for whom food is a bigger proportion of their spending,” he told me. But isn’t this all more “Project Fear”? His response: “Very quickly people will see it is not Project Fear but Project Reality – this is complete madness.”

Jacob Rees-Mogg and other Brexiteers have suggested the UK could simply apply 0 per cent tariffs to goods coming from the EU – but there is no guarantee that, if there is no deal, we will get 0 per cent tariffs in the opposite direction on the goods our firms are selling into the EU. This supermarket executive – who is one of the most respected people in UK business so knows a thing or two about dealmaking – told me on that point that “if you simply unilaterally say you are going to have low tariffs, you have no leverage” when it comes to making an agreement.

Other Brexiteers make the point that if we were to walk away without a deal and refuse to pay the divorce bill – as Brexit secretary Dominic Raab has suggested – this would give us leverage. This supermarket chairman took a very dim view of that suggestion as a strategy: if the UK did this, he said, “nobody would trust that we would keep our obligations as we go around the rest of the world seeking new trade agreements”. The point he makes is that if we renege on our financial obligations to the EU, no one will have faith that we will meet our obligations to them under any trade future agreement.

So this is the practical reality for households of a no-deal Brexit. The fact that we are no closer now to any proposition on Brexit commanding a majority in the House of Commons makes that no-deal scenario more likely. Remember, the Brexiteers asserted there would be a deal throughout the Vote Leave campaign – so whatever the government has a mandate for, it is not this.

There is good reason to believe that members of the British public realise this and want their democratic say on what’s going to happen to their country next. In the most recent You Gov Poll commissioned by the People’s Vote campaign (of which I am a part), 45 per cent of people now think there should be a vote on the final Brexit deal against 34 per cent who do not. This is a reversal of the view last December when just 33 per cent wanted a final vote, with 42 per cent opposed.

The poll also showed that, if they were given a people’s vote, 53 per cent of people now back staying in the EU with 47 per cent choosing to leave.

In-depth, constituency-level analysis carried out by Hope Not Hate and Best For Britain shows that more than 100 Westminster parliamentary constituencies that voted to leave in 2016 have now switched their support to Remain, including those of Boris Johnson (Uxbridge and South Ruislip) and Michael Gove (Surrey Heath), who co-led the Vote Leave campaign.

And, at the time of writing, more than 680,000 people have signed The Independent’s Final Say petition to give people a vote on the Brexit deal. The shift is undeniable and the momentum behind the campaign increases every week.

Of late there have been two attempts to undermine the efforts of the People’s Vote campaign. First, the usual nonsense that the campaign is London-centric, metropolitan and “elite”. This is simply not an argument that can be made with any credibility. The People’s Vote campaign has groups in every single part of the UK– the same cannot be said of the other side of the argument.

At the beginning of August, hundreds attended a packed rally in Bristol; this weekend just past more than 1,000 people took part in the rally in Edinburgh; and this coming weekend there is a big rally planned in Newcastle. Further events are taking place across the whole of the UK.

Second, there is the false claim – principally made by a minority on the left of UK politics – that the People’s Vote campaign is the forerunner to the creation of a new “centrist” party. This is ludicrous nonsense. The People’s Vote campaign involves activists and politicians from the three main parties, the Green Party, the SNP, Plaid Cymru and those of no particular party affiliation. The idea that Caroline Lucas’s Green Party, politicians from nationalist parties in Scotland and Wales and figures such as myself from the main parties in England are about to come together and create a new, big-tent party is patently absurd.

This is also an idea being promoted by Brexiteers who dislike the effective cross-party working there has been in and outside of parliament to thwart efforts to pursue the most extreme of Brexits – surely those on the left of British politics do not want to be parroting lines from the Brexiteer hard right?

It’s clear what the Brexiteers’ game plan is. The prime minister’s Chequers proposals, as I have said before in this column, pleased no one. Unless the hardest of Brexits is adopted by the government – which I do not believe could command a majority in the House of Commons – those Brexiteers will whip up xenophobia and campaign in the ugliest possible way in an effort to build support for a no-deal Brexit, which they continue to insist will not cause the catastrophic damage to jobs and livelihoods as many predict.

Research shows that the British public trusts economists most concerning Brexit predictions, then business leaders, followed by public service professionals such as teachers, doctors and nurses.

The British Medical Association, the Royal College of Nursing and the Royal College of Midwives are all backing the People’s Vote campaign, not least because they believe a no-deal Brexit will be deeply damaging to the NHS.

The government didn’t want us to see the analysis its own economists have provided to ministers on the economic impact of Brexit, but following the leaking of such details in January we know that their judgement is that the UK will be worse off in every single scenario, particularly if we left with no deal – in that scenario, trading with the EU on World Trade Organisation terms, it is estimated economic growth would be reduced by a whopping 8 per cent over 15 years.

The bosses of large companies such as Airbus and Jaguar Land Rover – which employ hundreds of thousands of people directly, and which indirectly provide hundreds of thousands of jobs in their supply chains – have also said that leaving the EU without a deal would be immensely damaging. JLR’s CEO, Dr Ralf Speth recently said: “If the UK automotive industry is to remain globally competitive and protect 300,000 jobs in Jaguar Land Rover and our supply chain, it must retain tariff and customs free access to trade and talent with no change to current EU regulations.” You can’t get much clearer than that.

All of this simply reinforces the necessity for the British people to be the final arbiters of what happens on Brexit – that is why so many people have been rallying behind the People’s Vote movement and Final Say campaign this summer. Long may it continue, for the good of us all.