The UK has allocated more than £100m to charter ferries to ease “severe congestion” at Dover in the event of a no-deal Brexit, as the government ramps up its multi-billion contingency plans.

Increased border checks at ports after Brexit could “cause delivery of critical goods to be delayed” if the UK leaves with no deal, according to documents outlining the £107.7m agreements to secure extra lorry capacity.

The Liberal Democrats described the move as “complete madness” and said the government was spending public money recklessly in a last-minute attempt to prepare for a no-deal outcome. As much as £2bn has been allocated for contingency plans.

The DfT did not put the contracts out to tender, as is customary. It said it was responding to a “situation of extreme urgency” brought about by “unforeseeable events”. The BBC reported that there was a private negotiation process after a number of firms were considered.

The French operator Brittany Ferries, the Danish company DFDS and the UK’s Seaborne Freight would step in to ease pressure on Dover in the event of no deal, allowing almost 4,000 more lorries a week to come and go.

The additional crossings are believed to be the equivalent of about 10% of the current traffic on the Dover Strait, and ports in Poole, Portsmouth, Plymouth, Immingham and Felixstowe will be used to ease the burden on Dover.

DFDS was awarded a contract worth £47.3m, and Seaborne a £13.8m deal. Brittany Ferries’ contract is worth £46.6m, with the company adding 19 return sailings to three routes between the UK and France. In a 50% increase of its current schedule, more sailings will travel between Roscoff and Plymouth, Cherbourg and Poole and Le Havre and Portsmouth.

The DFDS chief executive, Christophe Mathieu, said: “Our priority is to prepare for a no-deal Brexit and to create additional capacity. By increasing the number of rotations on routes like Le Havre-Portsmouth we will be able to meet the Department for Transport’s Brexit requirement.

“We will also work hard to minimise impact on existing Brittany Ferries freight customers and passengers, although there may be some changes to some sailing times, for which we apologise in advance.”

A Liberal Democrat spokesman said: “It is complete madness to see the government recklessly handing over £100m on preparing British ports for a no-deal scenario. The government has the power to stop no-deal at any time but instead is spending millions on last-minute contracts.”

Eloise Todd, the leader of the Best for Britain campaign for a second EU referendum, said: “The truth is no deal is not inevitable. This government has a real choice to make for our country and it does not have to toy with a cliff-edge Brexit.

“The only way forward for the country right now is to put the decision back to the people and put the public at the heart of the decision over our future. People have been locked out of the Brexit process since the 2016 vote. It’s time to bring them back in and let them decide our future.”

A DfT spokesman said: “This significant extra capacity is a small but important element of the Department for Transport’s no-deal Brexit planning.

“While remaining committed to working to ensure a deal is reached successfully, the department is helping ensure the rest of government are fully prepared for a range of scenarios, including a particular focus on a potential no-deal and to mitigate the impact of any Brexit outcome on all transport modes.”

The DfT has previously said the delivery of critical goods could be delayed as part of “significant wider disruption to the UK economy and to the road network in Kent” if EU countries were to increase border checks following a no-deal Brexit.

• This article was amended on 1 January 2019 to reflect the fact that £100m had been allocated on extra ferries rather than spent.