Revenue has said that 76% of goods being imported through Dublin Port from the UK are now being given green clearance, which is up from 45% one week ago.
Speaking at a multi-agency Brexit briefing at Dublin Port, Tom Talbot, Head of Customs Operations at the port, said the remaining 30% are being routed to orange or red channels where further documentation and checks are sought before leaving the port.
"The majority of those is documentation - so it is the wrong documentation or lack of documentation, and it is a quick call, we sort out the documentation and they move on their way," Mr Talbot said.
"Now the length of time they are with us very much does depend on that engagement from the importer, the haulier, the customs agent, are they there, can they sort that out."
Mr Talbot acknowledged that trade volumes continue to be low in comparison to normal for this time of year, due to stockpiling ahead of January 1, it being a quieter time of the year and Covid-19 restrictions.
He said the volumes have been slowly but steadily rising since last week and are now reaching up to 700 movements a day.
However, he added that there are no hard figures available yet to compare volumes in the last week to a normal year.
Mr Talbot said there is space for up to 250 trucks to park in Dublin Port and so far the maximum number reached has been 70.
Usually, there is no more than 30 or 40 at any one time, he added.
"So that's evidence that businesses are coming to terms with new procedures and with new customs declarations," he said.
He said the difference in experiences between those businesses who have prepared and those that have not is quite stark.
In relation to reports that some freight companies are moving goods from the UK into Ireland via the north to avoid delays, Mr Talbot said the movement of goods into Ireland from Great Britain are regarded as imports and customs rules equally apply.
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Trade organisations and Brexit customs experts though have warned that although goods are moving through Irish ports relatively smoothly so far, there is widespread and growing concern about the impact new procedures and systems are having on trade.
Those involved in importing say it is growing increasingly difficult to get goods out of the UK due to poor preparation by British companies who don't understand the new requirements, leading to customs delays.
Many smaller Irish firms have also emerged as either underprepared or not prepared at all for Brexit, despite the long lead in time and constant warnings from experts and the Government.
The Freight Transport Association of Ireland (FTAI) said its members are working hard to get to grips with the new procedures, but ongoing collaboration with state agencies is required.
It has also urged authorities to consider introducing additional easements to make it simpler for companies to navigate the new systems.
"It is a massive learning curve, one which we had half expected, but seeing it is believing it," said Aidan Flynn, FTAI general manager.
"The biggest issue for all parties is the amount of change that is expected in such a short amount of time."
"Industry hasn't had a chance to trial any of the new systems, the new customs systems, import export systems, pre-boarding notification systems, and it is a real learning curve as we go through the first couple of weeks of 2021."
The FTAI also says that despite the increase in direct ferry routes to continental Europe there is still not enough capacity to enable freight companies to bypass the UK landbridge.
Exporters also say they are experiencing difficulties, with one Dublin business revealing that it has 700 deliveries worth €70,000 currently stuck in UK customs, despite the fact it had spend thousand of euro in updating its systems in advance of Brexit, testing them and training staff.
"It is very frustrating, especially when we have put all the time, money and effort into getting prepared," said Daniel Plewman, co-founder of Happythreads, which supplies hospital scrubs and other personal protective equipment into the UK market, as well as in Ireland and France.
"Our brand, the Happythreads brand is at stake here, we compete in a very competitive market in the UK, we competing against domestic UK businesses who have no trouble shipping their goods. So we are really on the back foot here, and we have got to find solutions."