The new Brexit Secretary David Davis has insisted Scotland cannot have a veto over any deal to leave the EU despite Theresa May suggesting all of the UK should agree a unified approach.
Speaking on Sky's Murnaghan show, Mr Davis said the UK will be left with a land border with the EU in the Republic of Ireland that will create difficult issues, and it would be a mistake to create another border in the north too.
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He said: "I don't think that works. One of our really challenging issues to deal with will be the internal border we have with southern Ireland, and we are not going to go about creating other internal borders inside the United Kingdom.
"The aim here is to try to address the concerns of people who are basically Remain people, who say 'well we are worried about inward investment, we are worried about trade with Europe, we are worried about all sorts of things'.
"And we will try as best we can - they can't have a veto because there are 17.5 million people who have given us a mandate, they have told us what to do, we can't disobey it - but what we can do is to try to do what we can to minimise any disruption or turbulence or problems."
He also suggested that Article 50, the legal process through which the UK would officially set the clock ticking on its two-year Brexit negotiations, would be triggered "early next year".
His remarks paint a different picture of Brexit than that presented by the new Prime Minister, who has said she will try to build consensus before launching formal negotiations.
On Friday, Mrs May told Ms Sturgeon she would not trigger Article 50 before getting a UK-wide agreement.
Mr Davis, who is part of a triumvirate of Brext-backing new Cabinet ministers alongside Foreign Secretary Boris Johnson and the International Trade Secretary Liam Fox, has admitted that "even within government there'll be tensions" over the exit strategy.
Laying out the issues that lie ahead for Britain as it prepares to embark on the negotiations, he also warned that EU citizens may be blocked from staying in Britain permanently even if they arrive before the country leaves the union.
He said a "generous settlement" would be negotiated for EU migrants living in the UK and British citizens living in Europe.
But he warned this could attract a surge of EU citizens moving to Britain "in a big rush to try to grab a set of advantages that we are putting in place for people who have come here expecting us to remain with the European Union forever".
As a result, those who arrive after a set date could be blocked from being given an indefinite right to stay in Britain, he warned.
Mr Davis has also reasserted his belief that the EU would grant Britain access to the single market as well as a suspension of free movement rules, something which European leaders have so far ruled out.
His comments come after Australia called for a free trade deal with Britain as soon as possible in a Brexit boost for the Government.
In a Saturday phone call, Mrs May spoke to her Australian counterpart Malcolm Turnbull, who expressed his desire to open up trading between the two Commonwealth countries as a matter of urgency.
Mrs May said: "I have been very clear that this Government will make a success of our exit from the European Union.
"One of the ways we will do this is by embracing the opportunities to strike free trade deals with our partners across the globe.
"It is very encouraging that one of our closest international partners is already seeking to establish just such a deal.
"This shows that we can make Brexit work for Britain, and the new Secretary of State for International Trade will be taking this forward in the weeks and months ahead."
Former attorney general Dominic Grieve insisted MPs must have a vote on whether to trigger Article 50, which could give the Commons significant influence over the Government's timetable for leaving the EU.
"We undoubtedly do need a vote in Parliament," the Tory MP told BBC One's Sunday Politics.
"It's a matter of convention.
"The idea that a government could take a decision of such massive importance to the United Kingdom without parliamentary approval seems to me to be extremely far-fetched.
"It's not about law, it's about convention and reality."