All we need now is for Boris Johnson to praise Mark Field, the government-minister-cum-self-appointed-close-protection-officer who thought the best way to deal with a peaceful distributor of leaflets was to ram her into a pillar and grab her by the neck. If Johnson lauds Field as “my kind of guy”, then the already long list of similarities between Britain’s near-certain next prime minister and Donald Trump will get longer still. Compiling that list might once have been an amusing parlour game for politics nerds; now it is essential preparation for what is to come.

For Trump, you will recall, did not share the public shock at one of his party’s lawmakers using physical violence against a citizen exercising a basic democratic right. In the US case, the offender was Republican congressman Greg Gianforte, who bodyslammed a reporter – a Guardian reporter, as it happens – whose desire to ask a question irritated him. Trump offered no condemnation. Instead, the president said: “Any guy that can do a bodyslam, he’s my kind of guy.”

Still, we need not wait for Johnson to hymn Field’s prowess in manhandling the unarmed to spot multiple parallels between America’s current leader and Britain’s likely next one. The signature nest of blond hair; the political career forged by unexpected success on a TV show; the knack for grabbing attention by ensuring every public moment carries a frisson of danger, generated by the possibility that the rules are about to be broken, often through a remark that is crude or hurtful or both. Both men are skilled at making their appearances seem daringly, and therefore compellingly, unscripted – “seem” being the operative word in Johnson’s case. Note Jeremy Vine’s riveting account of watching the former London mayor deliver an apparently impromptu, even chaotically ad-libbed after-dinner speech – only to see him repeat the exact same performance, word for word, stumble for stumble, several years later.

More substantive similarities have been well documented. Both men have the same elastic approach to the truth that they had to their wedding vows. Trump’s lies are so legion, CNN has appointed a correspondent whose chief task is to tally them. Johnson’s form in this area is scarcely less impressive. The £350m on the side of the bus gets most of the attention, but let’s not forget the false claim that Turkey was on course to accede to the EU, a claim repeated by Johnson himself in a televised debate – only for him to deny earlier this year that he had so much as mentioned Turkey during the 2016 referendum campaign. In other words, he lied and then lied about his lie.

How do you oppose such a figure, one coated in Teflon and to whom the usual rules of political combat apparently don’t apply?

On Thursday, Johnson’s editor for a decade, Max Hastings, said, “I’m not sure he’s capable of caring for any human being other than himself,” words that have been said often of Trump, a man who seems devoid of basic human empathy. That was one reason why many Republicans vowed to stop him ever gaining power: “Never Trump” was their slogan. And yet, when the crunch came, they fell into line, so that today’s Republican party is entirely his creature. Likewise, many were the Tories who in recent years would earnestly tell any journalist within earshot that there was no need to worry, theirs was the army of ABB – Anyone But Boris – that they would coordinate in parliament and ensure Johnson got nowhere near the final two in a leadership contest. That resolve melted away the moment the Brexit party topped the poll in the European elections, prompting terrified Tory MPs to reach for a man they knew was, like Trump, wholly unfit to lead.

You can keep going in this vein, noting the uncanny similarities. But that’s only useful if we learn the lessons these last three years of Trump have taught us, if we use the US experience as a guide to what’s coming – and how to deal with it.

First, the Trump precedent suggests the notion of a new, tamed Johnson will prove to be baloney. Plenty in Washington assumed Trump would moderate once he was the Republican nominee and then, when that didn’t happen, once he was in office. He didn’t moderate. It would be equally naive to bank on Johnson discarding the shtick that got him to the summit once he reaches it. He might play benign Boris during this summer’s likely honeymoon period, but once things get difficult he’ll turn nasty, looking for whichever scapegoat he thinks might usefully deflect attention – and if that means baiting a vulnerable minority, say Muslim women, he’ll do it.

Second, the Trump and Johnson cases present a similar challenge: how do you oppose a figure to whom the usual rules of political combat don’t apply? It’s often said that the only person who can destroy Boris Johnson in the coming weeks is … Boris Johnson. Only a scandalous revelation could undo him. But would even that hurt? Think of the number of appalling stories that have emerged about Trump and how they have just bounced off him. What could actually surface about Johnson that the Tory faithful would not forgive or shrug off? Anything that would break a normal candidate – whether it’s adulterous affairs, drug use, racism or lies – is seen by the devotees of a Trump or Johnson as just part of the rule-breaking brand. (That said, the former foreign secretary’s Teflon coating might be about to be tested, following the Guardian’s report of a “loud altercation” at the Johnson residence in the early hours of Friday morning.)

The Trump experience surely suggests it’s more effective to confront Johnson on his own terrain. Trump promised a wall with Mexico and said Mexico would pay for it: it could never happen, and it duly hasn’t. Johnson has promised two things that are equally impossible: a new Brexit deal, which Brussels will not give him, or a no-deal Brexit, which parliament will block. Challenge Johnson on that and he retreats into cake-and-eat-it nonsense: his latest bit of magical thinking was his suggestion on Tuesday that we can crash out without a deal, but enjoy a “standstill” on our current EU terms while we work out a new arrangement. You can try this at home: cancel your Netflix subscription, but tell them you want a “standstill” that will allow you to keep watching all the shows you like. See how that works out.

These are the arguments Jeremy Hunt – the Tim Henman of British politics, who surely has “Surrey” carved on his heart – should be pressing. He should also hit his opponent in his supposedly strongest spot. Johnson’s advocates speak of him as if he’s electoral catnip, irresistible to the public, even liberal and Labour-minded voters. Their evidence is those two London mayoral victories, the last of which was more than seven years ago. Those Tory optimists may not have noticed, but something happened between 2012 and today, something that rather took the bloom off the Johnson rose in the eyes of non-Tories. By heading the leave campaign, Johnson made himself toxic to a large slab of the electorate.

For proof, look no further than those members of Team Corbyn who walked with a spring in their step this week. They reckon they can bring millions of Labour voters otherwise disenchanted with Jeremy Corbyn, and who voted Liberal Democrat or Green last month, back home when the alternative in a Westminster election is Prime Minister Johnson.

Tories should take note. Yes, the blond maverick can excite your base. But he can also fire up your opponents, sometimes just as much. Republicans decided to take that gamble three years ago. Now Britain’s Conservatives are about to roll the same dice.

• Jonathan Freedland is a Guardian columnist