Britain's prime minister, Theresa May, is in Bahrain today for the annual summit of the rich autocrats' club, the Gulf Cooperation Council. As the official announcement from Downing Street excitedly points out, she is the first British prime minister – and the first woman – ever to attend a GCC summit.

Aside from the obvious concerns about rights abuses in the Gulf states there are even bigger reasons this time to worry about May's trip. Most alarmingly, she is threatening to open "a new chapter" in relations between Britain and the GCC – a move which she has explicitly linked to Brexit. Closer ties with the Gulf will ease the economic pain of extracting Britain from the EU, or so the theory goes. To quote Robert Nisbet of Sky News:

"If the prime minister is to achieve her ambition of Britain morphing into a globally connected free-trade Mecca [sic], untethered from Brussels bureaucracy, then the oil-soaked Gulf ticks plenty of boxes."

But to imagine that the Gulf can offer a better and more secure business environment that Europe – or anything close to it – is utterly delusional. In the Gulf, corruption is rife. The rule of law is tenuous at best and liable to be over-ridden at any moment from on high. Success in business owes more to having powerful connections than to free competition, and the bureaucracy of Gulf states would make anyone yearn for the bureaucracy of Brussels.

The GCC countries – Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the UAE – are currently Britain's third-biggest export market (largely in the form of weapons) and May apparently believes trade can be further expanded post-Brexit. This is a gamble, to say the least.

The prime minister is betting that Gulf rulers can be persuaded to spend more at the very moment when they are trying to spend less. In global terms they are still wealthy but they are no longer the free-spending Eldorado of May's imagination. All of them are facing economic pressures which could get worse rather than better.

Quoted on the Downing Street website, May says that in recent years Britain's relationship with Saudi Arabia and Bahrain hasn't felt as close as it is old: "I want to change that." She continues:

"There is so much we can do together – whether it is helping one another to prevent terrorist attacks, Gulf investment regenerating cities across the UK or British businesses helping Gulf countries to achieve their long term vision of reform. "No doubt there will be some people in the UK who say we shouldn't seek stronger trade and security ties with these countries because of their record on human rights. But we don’t uphold our values and human rights by turning our back on this issue. We achieve far more by stepping up, engaging with these countries and working with them to encourage and support their plans for reform."

Oh yes. While in Bahrain she will meet "young people" to talk about the kingdom's largely non-existent "progress on reform".

Never mind the problems these countries – Saudi Arabia in particular – have caused in Britain and elsewhere by fomenting sectarianism, religious intolerance and fundamentalist ideology; they can be partners in protecting our security. Even that becomes a minor quibble when the prime minister has a long-term plan for closer ties which is both politically misguided and strategically foolish.

May's gamble is predicated on a belief that these anachronistic but oh-so-friendly Gulf monarchies will remain in place indefinitely. No one can be sure that they will, and what might follow is anybody's guess.

The question is whether their so-called reforms will be enough to save them from disaster. Bahrain, whose king invited May to the Gulf summit, is a case in point. A Sunni minority regime governing repressively over a Shia majority and reluctant to cede power is scarcely a formula for sustainability.

Meanwhile the Saudi monarchy, for whom letting women drive is still too radical a step, has pinned its survival hopes on the hugely ambitious Vision 2030 reform plan. Past experience suggests it will fail and any serious attempts to implement it are likely to be opposed by large sections of the Saudi public.

The danger in this for Britain is that when the Gulf monarchies crumble – as they must eventually – the markets so eagerly cultivated by Theresa May will be disrupted or vanish as power changes hands. Worse, if the crumbling brings turmoil of the kind seen in Syria and Yemen, economic dependence could force Britain to intervene in support of the monarchies, thus placing itself once again on the wrong side of history.

These are natural hazards when you do business with dictators. And when you sell them weapons you can never be absolutely sure whose hands they will end up in. One of Britain's export successes of the early 1970s was the delivery of a new warship, now known as the Alvand, to another friendly autocrat in the Middle East: the Shah of Iran. The Alvand lasted considerably longer than the Shah and is now the flagship of the Islamic Republic's navy.

Rather than forging ahead with closer ties on the Gulf, Britain's long-term interests would be better served by hedging its bets and loosening them. But the stark realities of Brexit are pushing in the opposite direction.

Despite all that, there is something weirdly fitting about the sight of Theresa May hobnobbing with the Gulf's hereditary rulers while, back in London, her government is fighting a Brexit-related court battle aimed at giving the Royal Prerogative precedence over the sovereignty of parliament.