A Kent motorway is undergoing a series of closures as work begins on turning it into a potential lorry park to deal with the possible impact of a no-deal Brexit.

In the most significant practical work yet to prepare for the consequences of the UK crashing out of the EU, the M26 will be closed through the night until next week for site surveys before another set of closures in the month leading up to Christmas to install gates in the central reservation.

The works, which drew the immediate anger of the local Conservative MP, got under way as Theresa May assembled her so-called “war cabinet” to brief them on the state of Brexit negotiations.

The meeting took place amid growing concern in her own ranks that she is prepared to agree an indefinite customs backstop to ensure an open border in Ireland. Despite some signs that a deal was creeping closer, the meeting broke up with no clear indication that the terms of the withdrawal agreement would be immediately agreed.

The start of the work was not disclosed to the MP Tom Tugendhat, who criticised the transport secretary, Chris Grayling, for apparently reneging on assurances. Grayling said he was confident that the contingency measure would not be needed after Brexit.

Hauliers and business have long warned of the potential for chaos after Brexit without a deal to preserve frictionless trade with the EU.

The Department for Transport is developing plans under the codename “Operation Brock” to handle queues of thousands of trucks, should freight be unable to progress swiftly through the ports when the UK leaves the EU – possibly from March next year.

Work has already started on the M20 motorway, with further closures ahead, where the DfT has earmarked a 13.5-mile stretch between Maidstone and Ashford as a holding park for thousands of trucks. The four-lane southbound carriageway will be closed, while a two-lane contraflow will allow traffic to continue to the Channel.

Now it has been revealed that ministers are also planning to use the M26, a 10-mile motorway that links the M25 to the M20 in Kent starting 65 miles from Dover, to park more lorries.

Highways England said: “As part of wider resilience planning, Highways England has been asked by the Department for Transport to develop plans to utilise the M26 to hold heavy goods vehicles, should further capacity be required in the future.

“We will be undertaking site surveys on the M26 during October leading to the installation of two gates in the central reservation to support the safe management of freight in the future, if needed.”

Although Highways England would not comment further on the details of their plans, the gates suggest that a contraflow system and car park would also be operated on the Kent motorway. Drivers will be diverted around the M25 and M20 between 10pm and 5am, doubling the length of journeys.

The news emerged as the furious local MP told the Commons that Grayling and Highways England had assured him and constituents that no works were planned up until Wednesday, when the closures started.

Tugendhat, the MP for Tonbridge and Malling, said: “It’s come to a pretty pass when a member finds out that works have begun on a motorway to turn that motorway into a parking lot without consultation either with the local community or indeed with surrounding members.

“The M26 works started last night. I wrote to [Grayling] in April asking whether or not this would happen. I was assured that works were not planned and only yesterday was it confirmed to me that Highways England had said that is exactly what was planned, despite having told me the reverse only a week earlier.”

He called on the transport secretary to explain how planning permission was granted with “no consultation”. Locals believe the sudden closure could see many people choosing to drive on the parallel single-lane road through small villages in Kent rather than using the official diversion.

Grayling asked to meet Tugendhat to discuss the issue: “I do not expect any of the contingencies that we have in place for a no-deal Brexit to be needed, because I’m confident we will reach a sensible agreement.”

In 2015, disruption at Calais led to queues of lorries in Kent that were handled under Operation Stack, and the DfT has been searching for better ways to deal with stranded freight vehicles after roads were brought to a standstill. It has paid millions of pounds to the owners of the abandoned Manston airport in Kent as an emergency standby lorry park. While Operation Brock is still being drawn up as an interim measure, local council plans have shown that a dedicated lorry park is likely to be at least four years away.

About 4m lorries cross the Channel between Dover and Calais each year, and hauliers have warned that the slightest delays will result in huge queues. Rod McKenzie, the director of policy at the Road Haulage Association, said: “It’s important that the government make contingency plans for a no-deal Brexit, but the concern is that this may be too little, too late – and it may have an impact on the rest of the supply chain in the Kent area, quite apart from the total chaos at the Channel tunnel and Dover.

“We’re worried that if there is no deal by November, drivers are going to need permits, and make safety and customs declarations, which is disastrous. The government are finally getting their heads around the scale of it.”

But he added: “Turning motorways into car parks frankly doesn’t really help. It’s more congestion and more pollution, which we’re all trying to cut down on – it’s not good news in any shape or form.”

He warned that lorry parks would not solve the problem of just-in-time deliveries and perishable goods, and that they could spell appalling conditions for drivers: “Imagine spending 15 hours parked up on a motorway with no lavatory or wash facilities – the mind boggles.”