The UK has injected some urgency into resolving the conflict in Yemen, saying it is to table its long-awaited UN draft resolution demanding a ceasefire and peace process.

The move came amid US-based reports that the UK foreign secretary, Jeremy Hunt, had to fend off intense Saudi resistance to the move when he met Crown Prince Mohammed bin Salman in Riyadh last week. The reports claimed the prince “threw a fit” during late-night talks with Hunt.

Following the Hunt-Mohammed meeting, the UK had highlighted that the Saudis agreed to remove one of the stumbling blocks to UN-sponsored talks; it would allow 50 Houthi soldiers who had been wounded fighting the Saudis in Yemen to be taken to Oman for medical treatment.

Karen Pierce, the UK ambassador to the UN, said she would table the draft resolution on Monday, adding that Yemen “was a man-made crisis, and what man has created, man can resolve”.

The UK has been criticised for being the penholder on Yemen at the UN but being too close to the Saudis and their ambition to defeat the Houthis militarily, which the UK insists is unrealisable.

In the past few weeks the US has taken a more active stance on Yemen, calling for a 30-day ceasefire and signalling its displeasure at Saudi efforts to end the three-year civil war by defeating the Iranian-backed Houthis rebels, including by seizing the strategic port of Hodeidah through which up to 80% of aid flows. Nearly 8 million Yemenis are dependent on food aid.

The UN special envoy Martin Griffiths told the security council he thought peace talks could start in Stockholm by the end of the year. No talks have been held since 2016.

He said progress was being made on initial confidence-building measures, including prisoner and detainee exchanges. Any such agreements would be the first signed between the parties since the conflict began, representing a timely message of hope in “the forgotten war”, he said.

Griffiths said he would return to Yemen next week to see if it was possible to revive the idea of the UN taking over the administration of Hodeidah. He would also hold talks with the Houthi leader Abdul Malik al-Houthi on the terms of their involvement in the Sweden-based talks.

Saudis believe the Houthis use control of the port to smuggle in arms with which to attack Saudi and United Arab Emirates forces.

The security council also heard from the under-secretary for humanitarian affairs, Mark Lowcock, and the World Food Programme executive director, David Beasley.

Both envoys gave vivid accounts of the impact of the surge in fighting since the US called for an end to hostilities.

Beasley said there were dozens of severely ill and malnourished children, with around 50 cases arriving every day: “They only have room for 20. The rest? They go home to die.”

Lowcock said UN sources had observed nearly 800 separate incidents of shelling, armed clashes or airstrikes since 30 October, including an attack on a bus carrying civilians away from Hodeidah on Tuesday which killed seven people.

Critical civilian infrastructure has not been spared either. Hodeidah’s largest public hospital was attacked three times in the last week, forcing patients – some of whom were still connected to medical devices – to run into the streets. A second hospital was damaged when it got caught in crossfire as frontlines shifted around the city. Fighters took up positions inside the hospital and on its roof, putting the entire facility at risk.

Beasley said the price of basic food staples in Yemen had doubled in the past eight months, even as household incomes shrunk. “For a country that’s dependent on imports for the basic needs of life, this is disaster.”

Lowcock said Saudi Arabia had helped to stabilise the Yemeni rial by depositing $200m with the Central Bank of Yemen. This had helped pay for imports of food and other essential commodities, but substantially greater funds for humanitarian assistance would be needed, he said.