Marks & Spencer chairman Archie Norman has warned customers in Northern Ireland will face higher prices and “gaps in shelves” if EU customs rules come into force later this year.
Mr Norman said current “pointless” checks were threatening its business.
Grace periods, which would see checks increase, are to end in September.
“We're waiting to see how serious it's going to be but if it's anything like southern Ireland, and at the moment it's set to be, then it's going to be very, very serious for customers," he told the BBC.
He called for a "common sense approach to enforcement focused on the ends, which is protecting consumers, not the bureaucratic means".
He said it was not the rules of the customs union, which mean products have to meet EU standards, but the “absolute pettifogging, Byzantine” enforcement and implementation of those rules that is stopping products getting through.
He explained that the wrong colour of ink had seen shipments held from crossing the Irish Sea.
Mr Norman said about one fifth of the retailer’s food products were not on sale in the Republic of Ireland.
He said. “Of the product that does get through, about 40% is delayed - which means you lose freshness and shelf life. We think we’ll be wasting about 1,000 tonnes of food a year because of border controls.”
Marks & Spencer is a major employer in Ireland, with more than 4,000 staff.
In a letter to Brexit minister Lord Frost, Mr Norman said the current EU customs arrangements were “totally unsuited and were never designed for a modern fresh food supply chain between closely intertwined trading partners”.
The government is set to make a statement on how it plans to deal with the NI Protocol on Wednesday.
Under the protocol, Northern Ireland is still in the EU’s single market for goods.
Supermarkets which send products here from Great Britain are subjected to light-touch checks under a so-called “grace period” which delayed some of the new processes but which runs out at the end of September.
When sending goods to the Republic, Mr Norman said each truck has to be accompanied by “three books” of documentation and if there are inaccuracies - down to one page being in a blue typeface instead of black - the documents have to be sent back.
He said Northern Ireland trade could be similarly problematic once the current light-touch export checks end and said a view some politicians and officials have that things will “quieten down” is incorrect.
Specialist Christmas products won’t be sent to Northern Ireland for unless something changes, he said.
“I worry what will happen when a fifth of our products don’t arrive for Christmas,” he added.
M&S now employs 13 full-time vets who aren’t looking after animals but are just “ticking boxes”, he said.
“Every piece of butter in every sandwich has to have a certificate.”
The solution is to find a method to “properly execute the rules” with the European Union but in a way that would “protect customers, not bureaucrats”.
"Enforcement should be focussed on the risk,” he said.
“On something like butter or cream, there should be a monthly licence so we don’t have to produce a vet’s certificate every time.”
“If there’s a tiny issue on the documentation, instead of stopping the whole wagon, it should flow through - we should be obliged to correct the documentation retrospectively.”
He said sourcing products from Ireland instead of Great Britain would be likely to have an impact on price.
The EU has said a temporary Swiss-style veterinary agreement for Northern Ireland, in which the UK continues to follow EU agri-food rules, could be a solution, but it has been rejected by the UK.
Mr Norman said he would support the solution but said he accepts it’s “not as simple as that” for the government. He has written to the government requesting a meeting.
“What I put forward to Lord Frost is a plan for a variety of individual things that even without a veterinary agreement, would get the product through.
“You shouldn’t need vets in every factory approving every sandwich. That’s slightly ridiculous and very expensive and not in anyone’s interest. In our range of sandwiches of 49, only about 25 are getting into the Republic of Ireland,” he said.
Mr Norman said M&S was one of the largest UK-based retailers operating in Ireland and said they were committed to continuing to operate in Northern Ireland.
“We were the only major UK retailer that committed to trade and invest continuously through the Troubles,” he said. He added that last year, M&S invested more than £10m in the business in Northern Ireland.
In a statement to the BBC Number 10 said Mr Norman’s letter was a “stark warning” of “the fundamental problems with the Protocol”.
“That is why we need to urgently tackle these issues, to ensure there is minimal disruption to people’s lives in Northern Ireland, as the Protocol itself intended,” it added.