Hauliers are calling for a two week derogation from EU rules, in order to allow retailers, suppliers, freight firms and others involved in supply chains between Ireland and the UK to get on top of new Brexit systems and procedures for the movement of goods.
It comes amid growing concern about delays to the flow of goods across the Irish Sea and into Ireland from continental Europe, as all those involved in the process try to get to grips with post-Brexit changes.
"We need a derogation for two weeks to let the goods flows," said Eugene Drennan, President of the Irish Road Haulage Association, whose members are increasingly being caught in the middle of the growing confusion.
Mr Drennan said a rising number of freight and transport firms in the UK are now withdrawing their services into Ireland because of the problems.
If the situation continues, Mr Drennan warned, there may be more shortages of particular goods as stockpiles put aside by companies prior to the ending of the Brexit transition period start to dwindle.
The hauliers' representative said systems put in place by Revenue and others agencies are proving too cumbersome and too restrictive, requiring repeat information to be entered each time for example.
Mr Drennan said that once such recurring data had been entered once, "we shouldn't have to ever again upload it".
Some of the systems used by freight operators do not "talk" to each other, he also claimed.
The criticism came as the chief executive of supermarket giant Tesco acknowledged that it has experienced some disruption to supplies to the island of Ireland since January 1.
Marks & Spencer has also had difficulties in getting certain goods into both Northern Ireland and the Republic of Ireland in recent days, leading to empty shelves in some of its outlets.
Earlier this week a Revenue Customs official said that three quarters of goods arriving into Dublin and other ports around Ireland were now passing through without needing to be stopped and checked, up from 45% last week.
However, freight companies have argued that this does not reflect the true extent of the difficulties, as the volume of goods passing through Irish ports from the UK is significantly down on this time last year.
This is due to stockpiling, Covid restrictions and because many transport businesses are avoiding the UK landbridge when moving products into Ireland from continental Europe.
They say large amounts of goods are stuck at distribution centres in the UK, awaiting Customs and other clearances.
Ferry operator Stena has cancelled 12 sailings again over this coming weekend, because demand on its Irish Sea routes from Fishguard and Holyhead in Wales at off-peak times from Friday evening through to Tuesday morning is so low.
It has also temporarily relocated a larger vessel, the Stena Embla, from the Belfast-Birkenhead route to Rosslare to increase capacity on the Cherbourg crossing where demand is high.
