A famine inflicting “huge loss of life” could strike at any time in Yemen, as food prices soar and the battle rages over the country’s main port, the UN humanitarian chief, Mark Lowcock, has warned.

Lowcock said that by the time an imminent famine is confirmed, it would be too late to stop it. Accelerating economic collapse has caused prices of staples to increase by 30% at a time many millions of Yemenis were already finding it hard to feed their families.

Meanwhile, fighting over the port of Hodeidah has limited its capacity, shut down its grain mills and closed the main road inland towards the capital, Sana’a, threatening a lifeline that has allowed aid agencies to reach 8 million people and stave off famine so far this year.

“One of the things about what happens in famines is there’s a sudden collapse of which you get no notice,” Lowcock, the UN under-secretary for humanitarian affairs, told the Guardian on the eve of a UN general assembly meeting on Monday to discuss the Yemeni crisis. “When the collapse happens, it’s too late to do anything. There’s a huge loss of life very, very quickly. So that’s the issue we’re flagging.”

The offensive on Hodeidah is being led on the ground by forces from the United Arab Emirates (UAE) with Saudi air support. They are fighting Houthi rebels who have held the port since 2014. The UAE paused the attack at the beginning of July to allow time for peace talks, but the negotiations stalled and the offensive restarted on 7 September.

Facebook Twitter Pinterest Yemeni children look at corn cobs for sale at a market in Sana’a but prices have soared amid supply issues. Photograph: Yahya Arhab/EPA

Before the latest offensive, Hodeidah’s population was about 600,000, but Lowcock said it was unclear how many were still in the heavily bombed port city. UN agencies recently delivered food aid for 42,000 families in danger, which Lowcock estimated represented about a quarter of a million people.

The veteran British aid official said he thought it unlikely there would be a direct assault on the city centre but was concerned about the impact of the battle on supplies reaching further inland, in a country that is 90% dependent on food imports.

Fewer ships are docking at Hodeidah, its grain mills have been cut off behind the shifting front lines and the highway north to Sana’a is now contested and mined, closing it to food deliveries. Aid convoys now have to follow a more circuitous route along a much poorer road with wrecked bridges and craters from heavy bombing.

At the same time the devaluation of the rial is pushing food further out of the reach of ordinary people.

“And if you were using all your very, very meagre income to buy food and you can now buy 30% less, you know it’s a massive hit,” Lowcock said.

He denied a report on the Irin news agency that the UN had tried and failed to evacuate 5,000 civilians from Hodeidah in April this year.

“The idea that you would be engaged in an evacuation of Hodeidah city … it’s not the kind of thing that we would propose,” Lowcock said.

Facebook Twitter Pinterest Mark Lowcock warned that once the famine was confirmed it would be too late to stop it. Photograph: Denis Balibouse/Reuters

The Saudi-led coalition has been widely criticised for the persistently high civilian death toll from its aerial bombing campaign, and for the fact that its own investigative mechanism exonerated its forces in almost every incident.

However, Lowcock noted that the Saudis had admitted that the 9 August bombing of a bus full of children was “unjustified” and promised to hold accountable those who contributed to the error. He added that the coalition had largely managed to avoid hitting aid operations.

“There is now basically a good system [to protect] the aid operation from the military activities and we wouldn’t be able to run the enormous operation we run were it not for the fact that we have confidence that our sites, our accommodation, all our convoys, all our immunisation activities, all our other activities, will be protected and respected,” Lowcock said.

Saudi Arabia and the UAE have offered almost half the $2bn (£1.5bn) pledged for humanitarian relief in Yemen. Lowcock insisted, however, their role as major donors did not stop him from speaking out about the impact of their military operations on the Yemeni population.

He said: “The record speaks for itself on what we’ve done and I’ve made a string of statements on abuses and atrocities, directed at all sides.”