Prime Minister Theresa May defended the UK's unity in Edinburgh Friday on her first visit as Britain's premier but said she was prepared to discuss options for Scotland's post-Brexit EU ties.

Two days after taking office, May travelled north to try allay Scots' fears for their future in a country set to chart its own course outside the European Union (EU).

While 52 percent of voters across the UK voted to leave the EU, 62 percent in Scotland opted for Britain to remain in the bloc, triggering calls for a second Scottish referendum on independence.

May told Scottish First Minister Nicola Sturgeon she had made Edinburgh her first port of call to show how "very important" Scotland was to her.

"I want to get the best possible deal for the whole of the United Kingdom out of our negotiations for the UK leaving the EU," she said.

Questioned about Sturgeon's threat to organise another plebiscite on leaving the UK, two years after Scots voted to remain part of the kingdom, the Conservative leader said: "As far as I'm concerned, the Scottish people had their vote."

But she also signalled some flexibility on Scotland's demands to be allowed to chart a divergent course.

"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," she said.

May took office after David Cameron stepped down as premier in the wake of the Brexit referendum.

The vote result sent shockwaves around the world and sparked fears of an economic downturn, with Britain potentially facing exclusion from Europe's single market -- a key concern for Sturgeon.

The Scottish nationalist leader, who has been adamant that Scots cannot be taken out of the EU against their will, said she was encouraged by her meeting with May.

"I was very pleased that Theresa May said that she was absolutely willing to consider any options that the Scottish government now bring forward to secure Scotland's relationship with the European Union," she said.

European leaders have pressed May to move quickly in implementing Brexit, amid fears of the damage the continued uncertainty could do to the EU and the world economy.

May said she and Sturgeon had discussed the timescale for triggering Article 50, which starts the clock ticking on two years of negotiations to leave the bloc.

But she repeated that she would not be rushed into enacting the divorce.

After six years as Cameron's interior minister, the 59-year-old was viewed as a safe pair of hands to replace him, but started with a deep cull of some of her former cabinet colleagues.

She sacked long-serving finance minister George Osborne and Brexit-campaigning justice minister Michael Gove -- and stunned world capitals by appointing the often undiplomatic Brexit spearhead Boris Johnson as foreign minister.

Graduates of Eton and other elite private schools who made up half of Cameron's cabinet were forced to take a back seat in the overhaul.

Over two-thirds of the new cabinet attended state schools, in line with May's promise on taking office to "build a better Britain.... that works for everyone -- not just the privileged few."

"May's radical reshuffle stuns the old guard", said The Guardian newspaper's front page Friday.

But controversy over Johnson's appointment has overshadowed the start of her tenure.

Speaking at the French ambassador to London's Bastille Day party on Thursday, the flamboyant former London mayor insisted that Britain was "not leaving Europe."

"It would be geographically, physically, culturally, aesthetically, emotionally and historically impossible," he said, in a speech that received a mix of boos and cheers.

The referendum campaign exposed deep divisions in Britain, pitting proponents of open borders and shared sovereignty against those who feel left behind by globalisation.

On Friday, hundreds of people lined the streets to pay a final farewell to murdered opposition Labour MP Jo Cox ahead of her funeral in her constituency in Batley, northern England.

Cox, a "Remain" supporter, was shot and stabbed during the charged referendum campaign.

The local man accused of her murder gave his name in court as "Death to traitors, freedom for Britain".

Her assassination was the first of a British lawmaker in 26 years.