The sheer magnitude of the famine facing Yemen was initially underestimated by the aid sector, leaving food security experts rushing to update projections made at the UN general assembly a fortnight ago, sources have told the Guardian.

The speed at which the Yemeni currency plunged in early September, forcing food prices to soar, is being blamed for miscalculations that mean between 1.5 million and 2 million more people than initially thought are now at risk of famine.

Humanitarians warn children will be worst hit in what is being forecast as the world’s most lethal famine for 100 years with up to 14 million people at risk, according to the UN.

“The crisis in Yemen is so huge and of such magnitude, we have to be frank about whether we can together deal with what is facing us,” said Lise Grande, the UN’s humanitarian coordinator for Yemen. “We are literally looking at hundreds of thousands, maybe even millions of people who may not survive.”

Britain announced on Tuesday it would provide further aid to tackle malnutrition among Yemen’s children, with funding secured to help screen 2.2 million under-fives.

But the news was met with cynicism from one humanitarian organisation, which criticised the UK for providing aid with one hand and arms to the Saudi-led coalition with the other.

The UN’s humanitarian coordinator in Yemen, Lise Grande, visiting injured children in the northern province of Saada, in August. Photograph: Naif Rahma/Reuters

Yemen was plunged into civil war in 2015 after Houthi rebels – Shia Muslims backed by Iran – seized control of much of the country, including the capital, Sana’a. A Saudi-led coalition launched an air campaign aimed at restoring President Hadi’s government, with support from the US, UK and France.

The famine is being driven by economic factors caused by conflict, rather than a lack of food, experts say. The depreciation of the Yemeni currency has caused food prices to increase, while the soaring cost of fuel has made transport more expensive.

In addition, importers of basics such as cooking oil, rice, sugar and butter have been prevented from entering the country due to restrictions imposed by Yemen’s central bank based in Aden, territory controlled by its exiled government.

“Tens of thousands of destitute families, who were barely able to buy what they needed just a few weeks ago, can no longer afford to feed themselves at all,” Grande told the Guardian.

About 8.5 million people in the Middle East’s poorest country already rely on the World Food Programme to survive, including 1 million who receive cash assistance.

But if the current trend continues, as many as 5.6 million more Yemenis may need assistance to survive.

Grande said: “Things are deteriorating very, very quickly. The implications of this are enormous, and, truthfully, frightening. The reality is that time may be running out.”

The UN’s humanitarian lead, who met with key donors on Monday, said the agency was now scrambling to raise funds for emergency cash assistance.

Grande said: “One of the fastest and most effective ways of helping destitute families is to give them cash. This allows them to buy what they need, when they need it. Humanitarians are looking at ways to expand cash programmes as quickly as possible.”

Her comments came as a representative from the Norwegian Refugee Council criticised Britain for supplying arms to Saudi Arabia.

Suze van Meegen, a protection and advocacy adviser for the council based in Sana’a, said: “I anticipate the calls will come for international government to inject more cash into solving the crisis.

“But the crisis doesn’t lie with money. It lies in stopping the war. There is a duplicity in the UK, for example, where the British government is providing a lot of money to help us reach people with aid but it could get more bang for its buck if it just stopped selling weapons to Saudi Arabia.”

She said the worst of the violence is concentrated around Hodeidah city. “In the last few months we have seen half a million people flee the region. We are also very concerned about the safety of the port there, which is depended on for 70% of the food and fuel Yemen needs.”

Van Meegen said people are already starving to death in “very large numbers”.

“From our perspective we may as well consider ourselves already in famine. This time last year we warned that 8.4 million people were already on the brink of famine. The images now speak for themselves.”

She added: “There is direct violence but equally we are seeing slow systematic steps by both sides to undermine the economy. It means food is more expensive, it’s double the price it was even a few weeks ago.”

Since the offensive on Hodeidah began in June, the Norwegian Refugee Council has seen the nature of its work change. Where previously it was trying to help Yemenis through assistance with education and livelihoods, the focus has shifted to survival.

Van Meegen said: “Our focus is helping those people who have left home with nothing but a few items in a plastic bag with food and cash. The other thing we are doing is trucking water which is hard to come by and very expensive.”

Announcing Tuesday’s aid package the minister for the Middle East, Alistair Burt, said the money would help screen 2.2 million children under the age of five and provide urgent treatment for 70,000 of the most vulnerable youngsters.

“The UK is extremely concerned at the deepening humanitarian crisis … Children are suffering the most and are 12 times more likely to die from diseases. Today’s aid package will help identify cases of malnourishment earlier and provide life-saving care for those most in need,” he said.

He called on all parties to support the UN special envoy’s peace talks to find a political solution to end the conflict.

The Department for International Development said the aid package of £96.5m will fund the UN children’s agency, Unicef, to tackle malnutrition over three years. Some of the funding is from a £170m package announced for Yemen on 3 April.