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 per cent of voters across the UK voted to leave the EU, 62 per cent 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.
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."
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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.
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.
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.