THERESA May has offered Nicola Sturgeon a major role in talks over quitting the EU, in a move designed to bind the First Minister to taking a UK-wide approach to Brexit.

The two women, meeting at the First Minister's official Bute House residence in Edinburgh, cleared the room of staff and advisors and spoke alone for around 35 minutes with the fallout from last month's referendum at the top of the agenda.

Ms May, who visited Scotland on her first official engagement after succeeding David Cameron, insisted she is determined to hammer out a "UK approach and objectives" to Brexit before triggering Article 50 - the official move that will see Britain quit the EU within two years - and offered Ms Sturgeon a key role in agreeing a negotiating stance.

It leaves the First Minister committed to discussions over the UK’s exit from the EU, which is now inevitable despite her insistence that Scotland being taken out of the bloc against the will of its voters is “democratically unacceptable”.

Even if she wins agreement for key demands, likely to be maintaining access to the single market and rights of free movement under a possible a Norway-style ‘EU-lite’ agreement, it is inconceivable that an SNP leader could argue Scotland’s future is best served by remaining in the UK.

The new Prime Minister has also ceded ground by saying she is willing to consider options the Scottish Government puts forward for maintaining its ties with the EU, after the country opted overwhelmingly to remain but finds itself faced with the prospect of being dragged out on the back of votes from England and Wales. The concession came just 24 hours after her Chancellor, Philip Hammond, had dismissed the prospect of Scotland agreeing a separate relationship to the rest of the UK.

Following the summit, which saw a female First Minister come face to face with a female Prime Minister for the first time ever, both leaders hailed a "constructive" discussion, although Scotland's constitutional future remained no clearer.

Sources close to the First Minister confirmed that a new independence referendum remained "highly likely", and while there was a commitment to engage with the UK Government in efforts to find common ground before triggering Article 50, there is no willingness within the SNP to barter with the rights guaranteed by full EU membership.

Meanwhile, Ms May's advisors made clear that despite her desire to achieve a 'UK approach' before formally serving notice to quit the EU, this does not mean handing the Scottish Government a veto over a potential post-Brexit deal, and accepted that Ms Sturgeon may walk away from the talks.

One UK Government source denied that offering the First Minister the chance to play a pivotal role in negotiations, despite her lifelong commitment to independence, is an effort to call Ms Sturgeon's bluff by offering her a role in a process it may be in her interest to see fail.

The SNP leader also took to Twitter to deny that "anything we are saying is a bluff", continuing publicly to leave the door ajar to backing Scotland's continued position in a post-Brexit UK while keeping her options open over independence.

The UK Government insider said: "Let's face the reality of the SNP's position. Coming out of one union is not solved by coming out of an even more important one. If it was Alex Salmond, who is a gambler, it would be different. But unless events run away from her I don't think Nicola Sturgeon will call a referendum, when there isn't the desire for one among the general public and it isn't certain she can win.

"Our position is that we want the best deal for Scotland and the best deal for the UK. When we say we want to involve the Scottish Government we absolutely mean that. We take completely at face value what the First Minister has said."

The Prime Minister, who was greeted by Ms Sturgeon on the steps of Bute House at around 12:30pm and departed around 45 minutes later, described her meeting as "excellent" and said she was keen to visit Scotland so early in her tenure to demonstrate how "very important" the country is to her.

Asked if Scotland could have a different relationship with the EU than the rest of the UK, Mrs May said: "I want to get the best possible deal for the United Kingdom out of our negotiations for the UK leaving the EU, but I'm willing to listen to options.

"I've been very clear with the First Minister today that I want the Scottish Government to be fully engaged in our discussions and our considerations, and I will listen to any options that they bring forward."

Ms Sturgeon, who has set up a council of advisors to consider ways in which Scotland can protect its relationship with the EU post-Brexit, said that despite differences politically, she believed she could develop a "good working relationship" with Ms May, saying the pair "approach business in a similar way".

She said: "The process that is now taken forward by the UK Government will be open and flexible and the Scottish Government will be fully involved in that.

"These negotiations have yet to take shape and the UK Government don’t yet know exactly how they will proceed from here, but there is an agreement that Scottish Government officials will be very closely involved in discussions to give shape to this process and will be involved in that process. Crucially, and this is the most important point from my point of view, is that that process will be open to considering options that the Scottish Government brings forward."