The Welsh and Scottish governments have called Theresa May's plan for the UK's departure from the EU not "consistent with the national interest".
They issued a statement urging the prime minister to pledge to stay in the EU's single market and customs union.
Ministers from Cardiff and Edinburgh join the UK and Irish governments later for a British Irish Council meeting.
The UK government said it was committed to maintaining a good working relationship with the Welsh Government.
Before the meeting in Guernsey, the cabinet office minister said despite the "inevitable political noise" as the UK prepares for Brexit, he would "ensure that we maintain the depth of our ongoing engagement" with the devolved governments.
David Lidington said: "Working together is exactly what people all across the UK want to see their respective governments doing. They want to see their lives being improved through joint endeavour.
"They don't expect different governments - with politicians from different parties - to agree on everything.
"But they do expect us to keep talking - and listening - to each other, and to co-operate on the big issues that affect us all," he added.
Mr Lidington's message was directed in particular towards the Scottish Government, which has failed to reach agreement with ministers in Westminster over issues relating to devolution after Brexit.
The UK and Welsh governments struck a deal over the long-running Brexit "power-grab" row relating to the EU (Withdrawal) Bill back in April.
But Wales' first minister disagrees with Downing Street on the best course for the UK's departure from the EU.
In a speech in London last week, Carwyn Jones called on Theresa May to "come clean" on Brexit and put the national interest ahead of her party.
He and Scottish First Minister Nicola Sturgeon have joined together to make a similar call ahead of the British Irish Council meeting, saying that the prime minister's plan to leave the EU's single market and customs union is increasingly difficult to reconcile with her "position on issues such as customs arrangements and regulatory alignment".
But they both said: "She cannot come clean because she is held hostage by the Brexiteers in her cabinet and party. This cannot continue.
"We call on the UK government in its forthcoming White Paper to commit to staying inside the single market and customs union recognising that this will require continued alignment with the EU regulatory environment."