Ministers have voiced concern that already stretched police resources will be diverted from Britain’s cities to help contend with any traffic and transport problems arising in Kent from a no-deal Brexit affecting the Channel ports.

The plans form part of Operation Snow Bunting, which aims to coordinate the policing response to Brexit, but Whitehall sources said there was unhappiness in cabinet with the idea of diverting so many officers to the county.

“I can’t believe we are planning to take officers off the street at a time knife crime is rising,” one cabinet source said, arguing that the public will start to understand the impact of a no-deal Brexit as the government finally spells out its plans.

On Wednesday morning, the government will say what tariffs it will levy on food and goods, and how it will ensure the Northern Ireland border remains open – plans that had been deemed so sensitive that they had been kept secret until now.

Theresa May told MPs after being defeated on her Brexit deal for a second time that ministers would publish “essential policies which would need to be put in place if we were to leave without a deal” before Wednesday’s Commons vote on allowing a no-deal Brexit on 29 March.

The prime minister said Conservative MPs would be given a free vote on the issue to head off a string of frontbench resignations. Cabinet members are expected to be split, with Philip Hammond, Amber Rudd and Greg Clark opposed to no deal and Liam Fox, Chris Grayling and Penny Mordaunt among those who could be in favour.

Kent police confirmed that they had requested more officers in the event of no deal, using an existing mutual aid system, but the force would not say how many officers it would need to ensure traffic kept moving.

Kent county council has drawn up plans to park 5,000 lorries on one lane of the M20, nearby dual carriageways and a further 6,000 at Manston airport if there are delays at the Channel ports.

But Paul Carter, the council’s Conservative leader, conceded the authority had not yet resolved how to handle tourist traffic via the Channel tunnel if disruption were to occur, and added that the UK would be heavily reliant on the response of the French.

“The authorities have promised that Calais will run smoothly and we hope it will, but there were long delays last week when there was a go-slow when they protested about a lack of resources to handle Brexit,” Carter said.

May herself is expected to support ruling out a no-deal exit on 29 March. Referring to Northern Ireland, she said she was conscious of “the potential damage to the union that leaving without a deal could do when one part of our country is without devolved governance”.

Neither Dublin, London nor the EU have published their no-deal plans for Northern Ireland because they have been deemed so sensitive.

Any warnings over the prospect of a renewal of violence or civil disobedience will be designed to concentrate the minds of the Democratic Unionist party and the Brexiters who voted against May’s deal.

Last month George Hamilton, the head of the Police Service of Northern Ireland, warned that border posts and security installations created as a result of a hard Brexit would be seen as “fair game” for attack by dissident republicans.

Hamilton also expressed concern that the disappearance of the European arrest warrant would mean fugitives could disappear across the border into the republic of Ireland with impunity.

In an interview with the Guardian last month, Hamilton described as “severe” the violent threat from the New IRA and other terrorist groups opposed to the peace settlement. A group calling itself the IRA claimed responsibility for parcel bombs sent to British targets last week.

Tariff schedules will have serious implications for businesses and farming in Northern Ireland which operate an all-island supply chain, forcing crippling costs on them.

The Home Office said: “The government is making preparations for all eventualities, including a no deal. In any Brexit outcome, the continued safety and security of both UK and EU citizens remains our top priority.”