Joining the dots between the death of a Saudi journalist in Istanbul and the possibility of a ceasefire in Yemen may once have seemed a stretch, but no longer.

Claims of the complicity of the autocratic Saudi crown prince, Mohammed bin Salman, in the murder of the Washington Post columnist Jamal Khashoggi, has weakened the chief architect of the war in Yemen and opened a new space for diplomats in which to operate.

That space may have been widened further by the surprise call on Tuesday by the US secretary of state, Mike Pompeo, for a 30-day cessation of hostilities.

The UN special envoy for Yemen, Martin Griffiths, has been touring the US, France and UK, against the backdrop of the unfolding drama of the murder and cannot be blind to its impact on western opinion and Saudi self-confidence. David Miliband, the former UK foreign secretary, told the BBC there was “a common link of the abuse of power” in the individual fate of Khashoggi and the millions of lives at stake in Yemen, which the UN has warned is sliding towards what could become one of the worst famines in living memory after three years of Saudi airstrikes.

It may seem illogical or frustrating both for those who have campaigned for three years against the Saudi prosecution of the war against Iranian-backed Houthi rebels, and equally for those that have argued Saudi Arabia is defending a legitimate UN-backed government in Yemen.

But history is full of individual moments that prove to be tipping points, especially if they are exploited with the skill of the Turkish president, Recep Tayyip Erdoğan. Information on the killing as yet undivulged to the public, but available to other capitals, is clearly making the Saudi royal court squirm.

One path to saving Prince Mohammed, the main Saudi ambition at this point, is to make other concessions, of which the west primarily wants three.

The first is for him to share power within the court. The recent arrival of other royal figures in Riyadh, such as Prince Ahmed bin Abdulaziz, King Salman’s only full brother, may be a sign of the return of a consultative court.

The second is to force him to reconsider Saudi Arabia’s unending boycott of Qatar, a country with vast gas assets, a huge US military base and arguably a better model for Gulf modernisation. There is no sign that is happening, however much Qatari diplomats plead the logic of such a course.

The third is to try to close the war in Yemen that the west repeatedly tells Riyadh it cannot militarily win, at least without horrific casualties and an intolerable famine that could leave as many as 14 million people, half the population, dependent on aid to survive.

Until now the Saudi plan has been to capture the strategic Yemen port of Hodeidah from the Houthis, and so control the flow of illegal arms, tax revenue and humanitarian aid. The Saudis have always said the capture of the port is the precondition for the Houthis realising they must talk.

Questions have been raised about when the UK first became aware of Pompeo’s call for a ceasefire. On Tuesday afternoon, after horrific firsthand evidence had been given by aid workers of Yemen heading towards a humanitarian abyss, the respected British Middle East minister, Alistair Burt, refused to shift UK policy.

Burt insisted no point would be served in calling for a ceasefire or banging the table, since such pleas would be ignored. He also put the blame firmly on the Houthis for the failure of the planned talks in Geneva painstakingly assembled by Griffiths.

The next day the prime minister, Theresa May, said the UK supported the US initiative. “We certainly ... back the US’s call for de-escalation in Yemen,” she told the Commons.

The UK is a bit-player in many conflicts, but not in Yemen. It is the second-largest arms supplier, and what is known as the penholder at the UN on Yemen, so is responsible for drafting any resolutions.

Some Tory MPs, notably Andrew Mitchell, the former international development minister, have for months been accusing the UK of abusing its penholder status not to act as a neutral broker on Yemen, but instead a protector of a major participant. Some of this is unfair, since the UK was active in preventing a summer Saudi assault on Hodeidah, and has pressed for the supply lines to be kept open. It was also instrumental in the appointment of Griffiths, and genuinely regards the Houthis as the true and under-criticised culprits.

It may be that Pompeo’s blueprint collapses, due to the intransigence of local actors, but as the search for Khashoggi’s body continues many will hope that an end to the starvation in Yemen may yet be his greatest legacy.