Theresa May travels to Riyadh once again under intense pressure over the UK government’s Middle East policy, and specifically its support for Saudi Arabia’s brutal, and so far failing, two-year war in Yemen designed to reinstate the UN-recognised government of President Abdrabbuh Mansour Hadi and oust Iranian-backed Houthi rebels from the capital.

The prime minister has promised to press Crown Prince Mohammed bin Salman specifically on the issue of blocking aid in Yemen, but do not expect a démarche. Denouncing a Saudi potentate in public is not a short cut to influence.

British ministers have already withstood relentless pressure in parliament and the UK courts to end arms sales to Saudi on the grounds that UK weaponry is being used in an air campaign over Yemen conducted in breach of humanitarian law.

But in recent weeks the political heat has redoubled, first as new pictures of starving Yemini children returned to UK TV screens, and then as the Saudis mounted an all-out blockade of ports and airstrips used to deliver aid. The Saudis said the naval and air blockade – as opposed to the naval inspection system in place since 2016 – had been mounted in response to an Iranian-supplied missile being fired by Houthis close to Riyadh international airport.

“How would you respond if Iran fired a missile at Heathrow?” the Saudi foreign minister, Adel al-Jubeir, told reporters on Tuesday, adding he had shown the British, Americans and the UN that the missile was Iranian supplied and had a range of over 560 miles (900km).

The Saudis have been spoiling to close down the Houthi-controlled Hodeidah port for months, but mainly private international pressure had forced Riyadh to hold off from mounting the planned air raids. But the missile attack gave the Saudis a plausible excuse to close Hodeidah.

Critics say it is a submit or starve strategy, and amounts to collective punishment of the Yemini people, many of whom are already starving to death. Al-Jubeir counters that the Houthis have been using the port to smuggle disassembled arms, and to seize humanitarian aid to sell on to the black market.

The Saudis want full checks on boats, saying the previous UN-backed inspection regime has been largely worthless or under-used. Al-Jubeir claimed no blockade had been imposed, pointing out that government-controlled ports remained open.

Al-Jubeir was speaking after a meeting in London of the so-called Quint, an anomalous body of two combatants, Saudi and the United Arab Emirates, and two of its arms suppliers, the UK and the US, plus Oman. Representatives of the UK-recognised government of Yemen did not attend, although the UN special envoy did.

If the British foreign secretary, Boris Johnson, mounted a private assault on the Saudi role in what he has described as “the world’s worst humanitarian crisis”, and specifically the need to reopen commercial as well as humanitarian shipments, he had little effect.

The reality is that Yemen has become yet another proxy in the interconnected contest between Iran and an ever more assertive Saudi Arabia across the Middle East, one in which it is increasingly difficult for Europe, let alone Theresa May, to find its foothold. The absence of persistent US diplomatic involvement makes matters worse.

Parts of the foreign office are privately anxious about the conduct of Saudi’s impulsive foreign policy. The UK remains committed for instance to the Iran nuclear deal, and would wish the Saudis did less to urge Donald Trump to tear it up. Saudi and UAE’s largely fruitless blockade of Qatar has left ministers scratching their heads and frustrated that their plans for a post-Brexit trade deal with the Gulf Co-operation Council lie fallow.

Equally, the enforced resignation, and de-resignation of the Lebanese prime minister, as much to do with Hezbollah’s influence on the Houthis in Yemen as in Lebanon, portray the Saudis as impulsive and disruptive, as opposed to a strategic force.

But faced by the unwelcome choice between the lesser of two evils, Theresa May’s instinct will be to choose Saudi over Iran, even if she would prefer the choice did not occur as often as it does.