In a joint statement, the Scottish and Welsh leaders said quitting was not in the national interest and urged Theresa May to secure a Norway-style solution in the EU exit talks.
The call comes ahead of a meeting of the British-Irish Council (BIC) in Guernsey on Friday, which will bring the leaders together with Mrs May’s deputy, David Lidington, and Irish Prime Minister Leo Varadkar.
Mr Lidington insisted the UK Government was committed to maintaining a good working relationship with the devolved administrations despite the “inevitable political noise” over Brexit and urged the Scottish Government “to maintain their own side of that relationship”.
Ms Sturgeon and Mr Jones said the European Union had been “very clear” that the UK Government’s red lines meant the “only Brexit on offer is one which will deeply damage our economies and possibly jeopardise our security”.
They said: “In practice, the Prime Minister’s position on issues such as customs arrangements and regulatory alignment appears increasingly difficult to reconcile with the red lines, but 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.
“The aim should be a ‘Norway plus’ model on the basis that the red lines set out by the Prime Minister in her Lancaster House speech in January 2017 are not consistent with the national interest.”
Relations between Westminster and Holyrood have become increasingly strained over Brexit.
SNP MPs staged a Commons walkout in protest over the way the EU (Withdrawal) Bill had been dealt with and Ms Sturgeon said Scotland had been “treated with utter contempt”.
Mr Lidington said voters expected the governments across the UK to work together and highlighted how Scotland had voted to remain part of the Union.
He 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.
“The UK Government, for its part, is committed to keeping up the pace, and improving the depth, of our co-operation.
“Whatever the inevitable political noise as we unpick the complexities of our membership of the EU, I will ensure that we maintain the depth of our ongoing engagement with the Scottish Government, including this week at the British-Irish Council in Guernsey.
“I hope that the Scottish Government will maintain their own side of that relationship.”
The BIC brings together representatives of the Irish and British governments, the devolved administrations in Northern Ireland, Scotland and Wales and the Isle of Man, Guernsey and Jersey crown dependencies.
The council will also discuss the current political situation in Northern Ireland and Mr Varadkar is expected to reiterate his regret that Northern Ireland has no representation because the Executive has still not been restored.
A UK Government spokesman said: “When we leave the EU the whole of the UK - including Wales and Scotland - will be leaving the customs union and single market. There is no change to that position.
“Leaving the customs union means for the first time in 40 years, the UK will have the freedom to strike our own trade deals.
“Our focus is on getting the best deal possible for the UK - one that allows us to take back control of our borders, laws and money.”