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New border rules introduced last week are already creating problems for exporters and traders, say firms.
On Friday, Marks & Spencer became the latest company to warn of the administrative burden and increase in export costs to some countries.
Parcels firm DPD has already suspended some services and there have been warnings from seafood exporters.
One export trade body told the BBC there was a "growing problem and sense of unease" among its members.
Shane Brennan, chief executive of the Cold Chain Federation, which represents chilled transport and storage companies, said the emerging problems have come despite the amount of cross border traffic still being quite low.
"Trade flows are still only about 50% of what we would expect, but even at those levels we are seeing levels of confusion and delays," he told the BBC's Today programme. "The feeling is we are building to quite a significant potential disruption."
M&S said the new trade arrangements were creating "very complex administrative processes". The red tape burden, along with potential tariffs on some exports "will significantly impact our businesses" in Ireland, the Czech Republic, and France, the retailer said.
The retailer added that the free trade agreement with the EU would not mean extra tariffs on its core UK sales.
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Transport Secretary Grant Shapps said he continued to work with companies to ensure a smooth transition to the new trade arrangements. He also told the BBC that it was estimated only about 1% of trucks have turned up at ports without the correct paperwork.