Goods are flowing effectively between Great Britain and Northern Ireland, the Government said.
The end of the transition period has produced deep-seated structural problems which will not be quick to resolve, the Road Haulage Association (RHA) has said.
The Government must intervene with extra cash before jobs are lost at freight companies, the industry warned.
A UK Government spokesperson said: “Goods are flowing effectively between Great Britain and Northern Ireland and there is no disruption at Northern Ireland ports.
“The grace periods for businesses moving goods between GB and NI are in operation and working well.
“We are aware of specific issues related to moving mixed food loads, known as groupage, and new guidance is coming soon following a successful trial with industry.
“To ensure that traders have the support they need to adapt to the new practicalities, we have set up the £200m trader support service which provides free advice and support to businesses of all sizes.
“We are committed to working with industry and the Northern Ireland Executive to address any issues that arise.”
Volumes of trade from the rest of the UK to Northern Ireland has fallen sharply and many suppliers are avoiding the route.
Dozens of lorries have been left sitting in yards in Great Britain, the Road Haulage Association said.
Meanwhile, the UK Government is conducting bilateral negotiations with Ireland over easing pet travel restrictions between Great Britain and the island of Ireland.
SDLP MP Claire Hanna said the current situation causes “challenges” for pet owners but more acutely for those requiring guide dogs, and she asked if any mitigations are going to be put in place.
Environment Secretary George Eustice replied: “The primary purpose of these pet travel regulations is to control the spread of rabies and both Ireland and Great Britain have a very similar and very high health status on rabies having not had it in dogs previously.
“We, therefore, do think that there should be easements on this particular provision, we have argued with the commission that we should be listed in part one but we are continuing to make those bilateral negotiations with Ireland a priority.”