Jeremy Hunt is to make a fresh effort to keep the Yemen peace process alive as he faces pressure from Saudi Arabia and the United Arab Emirates to declare that the Houthis have failed to abide by commitments to move their forces from Hodeida.

The UK foreign secretary was due to host the Saudi and Emirati foreign ministers in London on Friday, as well as David Satterfield, a US acting assistant secretary of state and a Middle East veteran.

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The Iran-aligned Houthi rebels have held Yemen’s capital, Sana’a, and the port city of Hodeida for three years, but are facing a concerted coalition effort to dislodge them, coordinated by the UAE and Saudi Arabia. The Gulf states say they are seeking to restore the UN-recognised government of Abd Rabbu Mansour Hadi. But there are disputes between the UAE and the Saudis about Hadi’s legitimacy.

The war has claimed up to 70,000 lives, plunged hundreds of thousands into famine and there has recently been a fresh outbreak of cholera.

The UN-sponsored peace process has hit a succession of roadblocks since the two sides agreed in Stockholm in December to withdraw troops from around the strategic Red Sea port of Hodeida.

A truce around the town has partly held, even if both sides repeatedly log incidents of ceasefire breaches.

Quick guide The Yemen conflict explained Show Hide How long has the war been going on? Yemen has been troubled by civil wars for decades, but the current conflict intensified in March 2015 when a Saudi-led coalition intervened on behalf of the internationally recognised government against Houthi rebels aligned with the former president Ali Abdullah Saleh. The war is widely regarded as having turned a poor country into a humanitarian catastrophe. Riyadh expected its air power, backed by regional coalition including the United Arab Emirates, could defeat the Houthi insurgency in a matter of months but instead it has triggered the world's worst humanitarian disaster, with 80% of the population - more than 24 million people - requiring assistance or protection and more than 90,000 dead.

What is the cause of the war? Its roots lie in the Arab spring. Pro-democracy protesters took to the streets in a bid to force the president, Ali Abdullah Saleh, to end his 33-year rule. He responded with economic concessions but refused to resign. By March 2011, tensions on the streets of the capital city, Sana’a, resulted in protesters dying at the hands of the military. Following an internationally brokered deal, there was a transfer of power in November to the vice-president, Abd Rabbu Mansour Hadi, paving the way for elections in February 2012 – in which he was the only candidate to lead a transitional government. Hadi’s attempts at constitutional and budget reforms were rejected by Houthi rebels from the north. The Houthis captured the capital, forcing Hadi to flee eventually to Riyadh. Photograph: Mohamed Al-Sayaghi/X03689

The UN special envoy for Yemen, Martin Griffiths, has travelled to Sana’a and Hodeida to clear the blockages to the redeployment, and told the UN security council on 15 April that Michael Lollesgaard, a UN-appointed former general, had finally secured agreement to phase one of the withdrawal of forces loyal to the Houthis, a group who prefer to be known as Ansar Allah.

The International Crisis Group, a thinktank tracking the civil war, says the delay is primarily caused by a dispute between Hadi and Houthis over the nature of the force that should take over Hodeida. Hadi wants the forces to be drawn from the pre-2014 police force and coastguards, and for them to be supervised by the interior ministry. The Houthis’ interpretation is that current security forces – which include many of their supporters – will remain in the city and ports, with minimal changes, once military forces have been removed.

Hunt said at the start of the meeting: “This is a horrendous conflict and it is taking too long to turn the ceasefire agreed in Stockholm into a durable path to peace. While it is hugely welcome that both sides recently agreed the UN’s plan for the first phase of troop redeployments in Hodeida, this took two months after the initial agreement was reached in Stockholm – far longer than we had all hoped.”

The Saudis and UAE are almost trapped politically, aware that the prosecution of the war is causing immense damage to their reputation, and yet not capable of reaching a wider political agreement with the Houthis on Yemen’s future.

Some western diplomats say it is an unanswered question whether the loose Houthi military and political structures are capable of reaching an agreement.

Some also in retrospect question whether Hodeida was the right place to focus an initial agreement, since the port’s monetary and strategic value to the Houthis is so large that it is difficult for its leaders to withdraw in favour of a neutral force.

Helen Lackner, a Yemen expert, is one of many to note that the Stockholm agreement was “signed under heavy pressure, the very brevity and vagueness of the texts … are a reminder of the rushed process which brought them about”.

But there appears to be no US desire to set a deadline by which the Stockholm agreement must be implemented. The US Congress has voted to end US support for the war, a decision that has prompted a rare presidential veto by Donald Trump.