A lottery-style system could be used to allocate scarce haulage permits in the event of a no-deal Brexit, a Department for Transport paper has revealed.

The paper says hauliers will need permits if no deal is struck, and the number of European Conference of Ministers of Transport (ECMT) permits available will be severely limited. One estimate suggests there will be only around 5% of the total required.

The paper suggests there will be a element of chance as to which hauliers are offered the permits, to allow as many hauliers as possible to continue to operate.

Permits will be allocated on the basis of criteria including emissions levels, the number of international journeys made, the proportion of haulage that is international and the product carried.

But the DfT said allocating on those criteria alone would lead to an allocation solely for the biggest firms, forcing many smaller ones out of business.

The department says it has thus decided that its system for allocation will also include “a weighted random element to the scoring of applications”, which it says will give the highest-scoring operators “many but not all of the permits they applied for”.

The remaining permits will be “allocated to a larger number of operators who have also scored highly on the other criteria,” it says, which will give a fairer chance for small and medium-sized operators.

“We estimate that around four times as many operators will receive permits if an element of weighted random selection is included,” the paper says.

The former shadow transport minister Daniel Zeichner, a supporter of the anti-Brexit group Best for Britain, said: “This is yet another sector where Brexit is threatening absolute chaos.

“If haulage permits become a lottery to get hold of, I don’t think anyone will be thankful to have to wait longer for their new phone or to find their supermarket delivery doesn’t have half the things they ordered in it because they’re stuck in Calais.”

A leak has revealed that managers at the Environment Agency (EA) were given just 24 hours to name 75 staff to be sent to the Department of Environment, Food and Rural Affairs (Defra) to help prepare for a no-deal Brexit.

A National Audit Office report in September said Michael Gove’s department would not be ready for no-deal, with meat and dairy and chemicals exports especially threatened.

Defra is responsible for almost a fifth of all the Brexit-related workstreams across government, covering the food and chemical industries, farming, fisheries and the environment.

An EA memo headed “URGENT Action – immediate attention”, leaked to the Guardian, said: “We are gearing up our contingency planning for EU Exit and have been asked by Defra as a matter of urgency to provide staff.”

It was sent on 22 October, with staff asked to redeploy within a week. “We realise this is an extremely short deadline and that many staff will be on half term,” it said. “However, please do your best as part of our ambition to go the extra mile to help at this challenging time.”