Theresa May has been warned that denying Scots a vote between Brexit and independence will make the break-up of the UK "inevitable", despite her claims leaving the European Union will make Britain "more united".

Mrs May, speaking as Article 50 was triggered to formally start the departure process, stressed Holyrood and the other devolved governments should expect a "significant increase" in powers as a result of Brexit.

She repeated her pledge that no powers currently devolved will be removed from the administrations in Edinburgh, Cardiff and Belfast.

But with the Scottish Parliament having voted by 69 to 59 in favour of a second independence referendum, SNP Westminster leader Angus Robertson told the Prime Minister of the impact it could have if Scots are denied such a vote.

Speaking in the Commons, he said: "The Prime Minister says that she thinks Brexit will bring unity to the United Kingdom, it will not. On this issue it is not a United Kingdom and the Prime Minister needs to respect the differences across the nations of the United Kingdom.

"If she does not, if she remains intransigent, and if she denies Scotland a choice on our future, she will make Scottish independence inevitable."

In her Article 50 letter delivered to European Council President Donald Tusk, Mrs May stresses: "From the start and throughout the discussions, we will negotiate as one United Kingdom, taking due account of the specific interests of every nation and region of the UK as we do so."

She also said: "When it comes to the return of powers back to the United Kingdom, we will consult fully on which powers should reside in Westminster and which should be devolved to Scotland, Wales and Northern Ireland.

"But it is the expectation of the Government that the outcome of this process will be a significant increase in the decision-making power of each devolved administration."

Mr Robertson told the PM that 62% of Scots, and every local authority area north of the border, had backed keeping Britain in the EU in June's referendum.

Mrs May responded: "My constituency voted to remain in the European Union. The point is that we are one United Kingdom and it was a vote of the whole United Kingdom."

She insisted that in the wake of the ballot, most people want politicians to "respect that vote and get on with the job of delivering for everybody across the whole of the United Kingdom".

Scottish First Minister Nicola Sturgeon tweeted: "Today, the PM will take the UK over a cliff with no idea of the landing place. Scotland didn't vote for it and our voice has been ignored."

Mr Robertson also accused the Prime Minister of having "broken her word" after she promised an agreement would be put in place with the devolved administrations before Brexit was triggered.

The Scottish Government had put forward its own "compromise" proposals aimed at keeping the country in the European single market.

Mr Robertson said: "The Prime Minister could have said she would try to seek an agreement with European partners on the plan, which could have protected Scotland's place in the European market, but she didn't.

"The Prime Minister could have taken the views of the Scottish, Welsh and Northern Irish governments seriously and she could have reached an agreement before triggering Article 50 as she promised. She did not."

Amid noisy exchanges in the Commons, the SNP Westminster leader said his party had become accustomed to "members on the other side of the house being incapable of understanding that the people of Scotland voted to remain in the European Union".

He added: "The Prime Minister promised an agreement. There is no agreement. She has broken her word."

He said the UK Government had a mandate to hold a referendum on the UK's EU membership, and added: "We accept the result to leave in the rest of the United Kingdom.

"The United Kingdom is a multinational state, with four nations - and two of them voted to stay and two voted to leave, and all of the rhetoric from the Government benches does not paper over the gaping chasm that there is not unity in this so-called United Kingdom."

After Holyrood backed calls for a fresh independence referendum, Mr Robertson said Scots "should have a choice after the negotiations have concluded and that it not be kicked into the long grass and that democratic choice denied".

Mrs May has repeatedly said to the Scottish Government that "now is not the time" for a second vote on independence, saying it cannot take place while the Brexit process is under way.

But former SNP leader Alex Salmond questioned whether now is the right time for the Prime Minister to trigger Article 50, claiming her approach over the last nine months had left Northern Ireland "deadlocked", Wales "alienated" and Scotland "going for a referendum", while the English are "split down the middle" over Brexit.

Challenging her at Prime Minister's Questions, he asked Mrs May if she had "considered in terms of invoking Article 50 that now is not the time".

The PM responded: "What the UK Government is doing in invoking Article 50 is putting into practice the democratic vote of the British people on June 23 last year in a referendum."

She added there had been a referendum on Scottish independence in 2014, with voters opting to remain in the UK, and she told Mr Salmond that he and his SNP colleagues should "put that into practice".