As the UK races towards a potential no-deal Brexit, President Donald Trump is cheering it on. But Brexit – especially without a deal in place with the European Union – would be bad for the US-UK special relationship and would make the UK a much less important US ally.

The ramifications of Brexit – in particular without a deal with the EU that pleases everyone – could be explosive. It could hurt the UK economy at a time when Trump’s trade war and economic policies are increasing the risk of a global recession, and threaten the very integrity of the UK amid growing signals that Northern Ireland and Scotland would consider breaking away. Boris Johnson appears willing to drive Britain off this cliff come hell or high water, threatening a no-deal Brexit and saying that the UK will leave the EU by the end of October, “do or die”. Everyone hopes that the UK finds a way out of this mess, but the past few years haven’t provided much evidence to believe that it will end well.

Trump has long supported Brexit. He made that support clear during his presidential campaign and has expressed it repeatedly as president. Trump’s national security adviser, John Bolton, now appears to be doing what he can to ensure Brexit happens. When in the UK recently, Bolton tried to incentivise Brexit by dangling the possibility of a trade deal with the US after the UK leaves the EU, saying that the UK would be at the “front of the trade queue” for a deal.

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But that won’t happen. First, the politics in the US right now mean that it is incredibly difficult to pass any trade deals, even with America’s closest allies. Second, and more important, US congressional leaders have already signalled that a deal would be dead on arrival in Congress if Brexit affects the situation in Northern Ireland. As the speaker of the House of Representatives, Nancy Pelosi, said: “If Brexit undermines the Good Friday accord, there will be no chance of a US-UK trade agreement passing the Congress.”

In fact, the reality of a post-Brexit US-UK alliance could be just the opposite of the false promises being peddled by Trump and Bolton: the longer-term impacts of Brexit could include a significantly downgraded relationship between the two nations. It’s been a long time since the UK was the global power it once was, but it’s still a vital US ally. From diplomatic cooperation at the UN, to supporting the Iran nuclear deal, to working together in Nato, there are endless examples of how a strong alliance – and a strong UK – is in the US interest.

But if the UK leaves the EU – especially without a deal – its influence and power will decrease markedly. It would no longer be able to influence EU decisions on economic matters in a bloc that constitutes the world’s second largest economy and with which the US traded $1.3tn in goods and services in 2018. It would no longer be able to influence the EU position on challenges such as Russia and China. If a no-deal Brexit causes a rift within the UK by pushing Scotland towards independence or undermining the Good Friday agreement, it will have even less bandwidth to play a positive role around the world. And if Brexit damages the UK economy, it will likely mean a UK with less global economic and military power.

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While a post-Brexit UK is still likely to be one of the world’s largest economies and will retain its seat on the UN security council, it will be less important to US national security and economic interests. In addition, if the UK and EU remain at odds over significant economic and political issues in the wake of Brexit, it could place the US in an awkward position between close allies in the UK and on the rest of the continent.

Furthermore, Brexit won’t make the serious policy disagreements between the Trump administration and the UK magically disappear. For instance, the two have been at odds over the US withdrawal from the Iran nuclear deal and whether to allow the Chinese telecommunications company Huawei to do business in Britain. It seems unlikely that the Trump administration would be willing to give the UK a break on those issues in the event of Brexit – just look at the recent spat with Britain over whether to release an Iranian oil tanker detained in Gibraltar.

While some might believe that Trump and Johnson’s relationship as kindred demagogic spirits could help buoy the alliance in the wake of Brexit, it should be clear by now that the two leaders are driven by their own political interests and are willing to damage the special relationship if it advances their own personal positions.

Trump has no interest in the US-UK alliance – he’s an agent of chaos, and supporting Brexit is yet another way for him to upend international norms. Trump’s disdain for allies should be fair warning to those who think the president might be willing to offer fair trade terms to Britain. As analyst Jeremy Shapiro points out, what we know so far about the terms for a US-UK deal “reveals that it is very much an ‘America first’ effort”. Faith in Trump to help a US ally is misplaced. “Our allies take advantage of us far more than our enemies,” Trump said at a recent rally.

If the current UK government believes that the US will shower rewards on Britain in the wake of Brexit, or that it will somehow bail Britain out, they’re wrong. Many policymakers in America will stick with the UK because of the longstanding alliance, but it could be a diminished alliance. And that would be bad for both countries.

• Michael H Fuchs is a senior fellow at the Center for American Progress, and a former deputy assistant secretary of state for east Asian and Pacific affairs