It is a rare opportunity. Seldom does the voting public have the chance to watch their elected politicians confront very specific false promises in real time. Usually, campaign promises are either too vague to be contrasted with reality — “Make America Great Again” — or too long term. By the time that “guaranteed growth” either arrives or does not, the person who said it would happen is long out of office.

But in Britain right now, something different is unfolding. During the referendum last year, politicians advocating their country’s departure from the European Union gave some specific assurances. Some derived from ignorance; as it turned out, few of them really understood how the EU works. Others were lies, which they knew to be lies at the time.

Because they did not expect to win that campaign, they didn’t expect either their ignorance or their dishonesty to be revealed. But then they won — and now it is happening.

The most egregious lie was about money. During the campaign, leading Brexiteers drove around the country in large red buses, emblazoned with a slogan “We send the EU £350 million a week, let’s fund our NHS instead.” This was a very influential argument, as the Brexit campaign managers have admitted. It was also an invented number: Britain does not send the EU £350 million a week, as fact checkers showed over and over. Some of those on the winning side admitted as much after the campaign.

But now, instead of receiving “£350 million a week”, negotiators are trapped in an argument about how much money Britain owes Europe — for budgetary promises not kept, for agreements signed and not honoured.

More ominously, the British Government is just now realising that leaving the European single market, which is far more than an ordinary free-trade zone, will cost it in other ways, too.

Jointly designed European agencies and arrangements may now have to be created again from scratch, at vast expense: pharmaceutical and nuclear regulators, for example. It is possible that a vast new customs service, complete with parking lots at the border, computer systems and customs agents, will be needed to cope with new tariff regimes once Britain is outside the European customs union. In the long term, Britain will have more bureaucracy and less money to spend on the National Health Service.

The second falsehood, frequently repeated during the campaign, was that leaving the single market would be fast, simple and easy. Liam Fox, now Britain’s top trade negotiator, said a new trade deal with Europe would be “the easiest in human history”. David Davis, now the minister in charge of the whole process, declared that “we can do deals ... and we can do them quickly”. With breathtaking insouciance and eye-watering obliviousness, others implied that all sorts of trading arrangements with countries all over the world could be ready in a matter of months.

In practice, more than a year has passed since the referendum and nearly six months have passed since Britain invoked Article 50, the “exiting the EU” procedure. During that time, almost no progress has been made. The British Government itself is divided about its own position, which makes it difficult to talk to Brussels. This past week, Davis told the House of Commons — to howls of derisory laughter — that “nobody pretended [Brexit] would be easy”. It is as if he has actually forgotten that he himself repeatedly pretended exactly that.

What happens next is unclear. We know that the Brexiteers’ promises were hollow. Their assessments were wrong. Whatever remaining credibility this government still has should have vanished.

Still, elections are complicated things, party loyalties are strong and there are other issues in play. During the referendum campaign, voters were not bothered by facts. During the recent snap elections, they seemed uneasier about the ruling party and refused to give it an absolute majority. Will the Brexiteers now be further punished at the ballot box? We shall see.

The answer matters because a parallel moment is about to arrive in the United States. As a candidate, Donald Trump also made some very specific electoral promises, including, for example, the construction of a wall along the Mexican border, to be paid for with Mexican money.

It did not matter how many Mexican politicians denied that this would happen; Trump kept repeating the promise. Now the budget battles are looming and, unsurprisingly, Mexico seems no more likely to pay for a border wall than Brexit is to free up £350 million a week for Britain.

Will Trump’s voters punish him for failing to do what he said he would do? We shall see about that, too.

• Anne Applebaum writes a biweekly foreign affairs column for The Washington Post