The head of the UK tax authority has warned that border and tax checks post Brexit could require an extra 5,000 staff with new customs checks costing the taxpayer up to £800m.

HMRC chief executive Jon Thompson warned that could take between five and seven years to get a new streamlined system to deal with imports and exports in place.

He told the Treasury select committee he was most concerned about the Dover- Calais route which cannot accommodate expanded customs checks warning it would take just two hours of disruption for “everything to stop”.

His comments come months after shipping, ports and business interests complained that the government wasn’t taking their concerns about Brexit gridlock seriously enough.

Thompson said HMRC was investigating the “business case” for a new Singapore-style system, which could deal with customs and border checks in one system.

He had hired the team that delivered the Singapore project, but said the Treasury would have to stump up between £500m and £800m to get it off the ground.

“We need to be transparent with you: that is a mega project,” Thompson told the committee. “You need to be thinking about that as a project that costs somewhere between £500m and £800m.

“It would take five to seven years to implement. We have been asked to look at whether there is a business case for that because there would be a noticeable change to GDP in my opinion.

“It would make it much smoother to import and export if you only had to go to one place instead of multiple different government departments.”

Another HMRC official told MPs on Thursday that in a “crude estimate” it could require an additional 3,000 to 5,000 people by the 30 March 2019 Brexit deadline, to meet the increased custom demands posed by Brexit.

Jim Harra, HMRC’s director general of customer strategy, said the organisation would have to deal with an additional 130,000 new companies after Brexit that import and export within the EU but do not currently come into contact with British customs.

This would involve a fivefold increase in business and require five times as many staff – possible up to 5,000 workers.

“There are probably about 130,000 new businesses that will be dealing with customs for the first time and there is a big challenge in reaching them, supporting them and getting them to be able to comply with their obligations on a transitional basis as well as on an ongoing basis,” said Harra.

Earlier this year the previous treasury select committee chairman Andrew Tyrie warned that confidence had collapsed in the HMRC’s capacity to deliver a new customs declaration system in time for Brexit.

Thompson said HMRC did not have the money or resources at this point to tackle the shift, but “extensive conversations” had been had with the Treasury on the issue.

Thompson said the authority may have to prioritise Brexit changes over existing projects to transform and improve the HMRC if it is to cope with Britain’s divorce from the European Union.

Asked which ports had the greatest potential for disruption, he pointed to the Eurotunnel system between Britain and France, saying: “Our major concern is the closed loop system that is between Dover and Calais, it is the area where we are focusing most.

“The situation on the other side of the Channel is more problematic,” said Thompson.

He said that while concerns have widely centred on Operation Stack – a traffic management tactic that requires lorries to park on Kent motorways when channel crossing is disrupted – there was “equally a risk of a French Operation Stack because you can’t get through Calais to get to Dover”.