Haulage firms are warning of "significant gaps" in UK border plans for the end of the Brexit transition period on 31 December.
Eight groups warned ministers that if issues were not addressed, the supply chain "will be severely disrupted".
Transport Secretary Grant Shapps said the government will work to ensure the "best systems are in place".
The government has also given itself powers to build temporary lorry parks in England without local approval.
The UK left the European Union on 31 January, but a transition period - where the UK continues to follow some of the bloc's rules - remains in place until 31 December while the two sides negotiate a trade agreement.
However, trade talks have been taking place since March and both sides have complained of little progress being made.
If a deal is not agreed and ratified by parliaments by the end of the year, the UK will go into 2021 trading with the bloc on World Trade Organization rules - which critics fear could damage the economy and cause issues at the border.
In a letter to the Cabinet Office Minister Michael Gove, seen by the Financial Times, the eight logistics organisations - including the Road Haulage Association - raised concerns over IT systems, the funding to train up customs agents and the pace of physical infrastructure being built.
They asked for an "urgent roundtable meeting" with Mr Gove, Chancellor Rishi Sunak and the transport secretary.
The letter urged ministers to take the concerns "seriously" and to "listen to the detail", or face supply chain issues after the transition period ends on 31 December.
It added that the coronavirus pandemic had demonstrated "the importance of a free-flowing supply chain", and that the supply chain must be protected ahead of a potential second wave of the UK epidemic.
'Crystal ball'
Mr Shapps said he regularly met the Road Haulage Association and wanted to reassure them "planning for the end of the transition period hasn't stopped" during the coronavirus outbreak.
He told BBC Radio 4's Today programme: "You can always look in the crystal ball and there will always be concerns about what if this happens [and] what if that happens.
"Our job is to work with people like the hauliers to make sure that we have got the best systems in place."
The transport secretary said he "could not pre-empt the outcome" of ongoing trade talks with the EU, which he conceded created "some uncertainty".
But, he said, the government had kept supply changes going throughout the pandemic and "we are absolutely confident we will do that again in the future".
Earlier this week, the EU's chief negotiator, Michel Barnier, said the UK was risking leaving the transition period without a deal unless it began to compromise.
He said he was "worried and disappointed" about the lack of concessions from his British counterpart, David Frost, after a trade deal meeting on Tuesday.
No 10 said it was "clear" that a deal "will not be easy to achieve".
Law change for lorry parks
The logistics industry letter came as the government gave itself powers to grant emergency planning permission for it to build temporary lorry parks and inspection posts in 29 councils areas across England, without the need for local approval.
The government said the lorry parks, which can stay in place until the end of 2025, would contribute to "an orderly transition to the new system of controls to secure the border" and would help to address the impact coronavirus may have had on port operators' ability to provide the necessary infrastructure themselves, in time for the end of the transition period.
Areas affected by the law change - brought about through a statutory instrument - include Cheshire, Lincolnshire, Liverpool, Devon, East Sussex.