The repercussions for the UK of a no-deal Brexit could be similar to the national emergency faced by Iceland during the volcanic eruptions in 2010 that brought parts of the country to a standstill, according to advice being given to civil servants.

The warning comes from the Cabinet Office, which is coordinating training for thousands of staff across Whitehall to help prepare departments for a disorderly departure from the European Union on 29 March.

The impact on Iceland from the volcanic ash clouds in 2010 is regarded as a useful example of the kind of escalating disruption that could face the UK this spring, according to those who have attended the closed seminars.

Staff have been told to look at the example of the eruptions from Eyjafjallajökull because they caused extensive disruption within Iceland that then reverberated across Europe. In particular, air travel was thrown into turmoil, with hundreds of thousands of people left stranded by cancelled flights.

The Cabinet Office believes this represents the “nearest recent example” of what government departments could have to cope with. But the potential disruption to the UK from Brexit is likely to be much broader, according to the government’s private planning assumptions.

The comparisons, and the lack of detailed preparations at the heart of government, are causing immense disquiet among some rank-and-file civil servants. “The level of planning required for no-deal Brexit is the same level as war planning,” said one Whitehall source. “A no-deal Brexit will have the same systemic impact. Iceland gives us hints and clues about what might happen, but Brexit is unlike anything we have ever seen.”

Though the government insists some high-level preparation for no-deal began last year, the Cabinet Office only recently considered providing training for the vast majority of civil servants, and a rolling programme began this month.

The contingency planning for no-deal – codenamed Operation Yellowhammer – has so far involved hundreds of civil servants being given a three-hour introductory briefing on the potential impact on communities, trade, border crossings and regulations.

The government has a running list of “reasonable worst-case scenarios”, which is constantly being amended and updated. Earlier this month it included a gamut of serious concerns.

According to an internal document seen by the Guardian, these included:

• A reduction in certain fresh foods and increases in prices, with people on low incomes disproportionately affected.

• Price rises across utilities and services including fuel.

• Private companies “cashing in” because they will put commercial considerations first.

• Police forces being stretched by the likelihood of protests and counter-protests, along with an increase in public disorder.

• Restocking of medicines becoming problematic after the first six weeks.

• Disruption of supplies to vets, which could “impact the UK’s ability to prevent and control disease outbreaks” among animals.

• A significant reduction in the flow of goods through Dover and Eurotunnel to as low as 13% of current capacity on the day of Brexit.

Another scenario is that the UK and EU will not have secured a data protection agreement before Brexit, which could prevent police from having instant access to information held by European forces on EU citizens arrested in the UK.

One concern focuses on how the government’s Cobra committee, which sits during times of emergency, will be able to make decisions before and after Brexit. While local authorities, agencies and health trusts have been making no-deal preparations, there is little understanding in Whitehall about what they have done, according to a number of sources who have spoken to the Guardian.

“Cobra can only take decisions if it knows what is going on at the local level,” said one. “It needs information that has been properly collected and collated. At the moment we don’t have that system in place.”

Another said: “We are having meetings for the sake of having meetings. There has been no proper oversight of what has been going on on the ground. So in many areas we are flying blind. It’s appalling and incredibly frustrating.”

He added: “There has been a lack of energy and a lack of urgency. The preparations for no-deal Brexit feel very unstable.”

One official told the Guardian the mood in Whitehall seemed to be that no-deal would not happen, or that if it did, it wouldn’t be as bad as some predictions. “Actually, the short-term impact could be worse,” the official said.

On Friday the chancellor, Philip Hammond, said there would be significant disruption to the UK economy if Britain left the EU without a deal.

“We will find ways of managing things like the additional time it takes for trucks to get through the border,” he told the BBC’s Today programme. “But it might take us quite a while to sort that out. So there will be a short-term impact through disruption. There will be a long-term impact through a reduction in the size of our economy.”

He added: “I clearly do not believe that making a choice to leave without a deal would be a responsible thing to do, but I recognise that that is potentially a default that we could find ourselves in.”

Asked about the comparisons between Brexit and Iceland’s emergency in 2010, the Cabinet Office said it was sensible to use examples as part of its extensive training programme.

A government spokesperson said: “The government remains committed to delivering an orderly withdrawal from the EU. Our high-level planning assumptions ensure we can responsibly prepare for all scenarios.”