Nicola Sturgeon should "get on with the day job" of running Scotland rather than "focusing on holding another independence referendum", Theresa May has said.

The Prime Minister addressed the issue directly for the first time since the First Minister revealed last week she wants to hold a second independence vote by 2021 if Brexit happens.

Speaking at Prime Minister's Questions on Wednesday, May accused the SNP of "ignoring those millions of Scots who do not want" a new referendum.

Sturgeon maintains that Scots, who voted 62% Remain in the 2016 Brexit vote, should have the option of independence if Scotland is forced out of the EU.

This should happen within the lifetime of the current Holyrood parliament, she told MSPs last week, which would mean a referendum before the next Scottish Parliament elections in May 2021.

Speaking to STV News last Friday, the First Minister also indicated a second independence referendum could still be an option even if the UK stays in the European Union.

Conservative Borders MP John Lamont opened PMQs by marking the 317th anniversary of the 1707 Act of Union, and asked May if Sturgeon is "obsessing with independence".

May answered: "I'm sure all members across this House will want to join me in marking this anniversary.

"He is absolutely right that under the SNP, the government in Scotland, what we're seeing is public services getting worse because the SNP are focusing on holding another independence referendum."

May added: "As my honourable friend says, it's time the SNP stopped ignoring those millions of Scots who do not want another independence referendum and got on with the day job, and focus on the issues that matter to people, like schools and the economy."

Sturgeon accepts she would need a Section 30 order from the UK Government to "put beyond doubt" the Scottish Government's ability to actually hold a fresh independence vote.

The Prime Minister has long stated she would not grant those powers to Holyrood, first refusing a Section 30 request from the First Minister back in the spring of 2017.

May was later challenged by SNP Westminster leader Ian Blackford to match the Scottish Government's pledge for free tuition for EU students.

He asked: "Will the Prime Minister follow this example, or is she determined to build a bigger hostile environment?"

May responded: "We have made clear about the position for EU students in this year and we will make the announcements in good time for students for future years.

"But I think I am right in saying what the Scottish Government has actually done is said that EU students can have free tuition up to 2024, but English students will have to pay."

Blackford replied: "Quite remarkable, because it is the Tories that have introduced fees for English students."

He said the UK Government's plans to cut EU student visas to three years would hit students studying in Scotland, where degrees are normally four years.

Asking for a visa extension to cover this, Blackford told May: "The Scottish Government and Scottish universities have asked repeatedly for this simple change to be made to reflect our circumstances."

May replied: "I understand the situation is not quite as problematic for those students as you set out, given the ability to convert these."