Theresa May is effectively "out of power" and would have departed Downing Street a long time ago under normal political circumstances, Nicola Sturgeon has said.

Speaking on the BBC's Andrew Marr programme, Scotland's First Minister also suggested that the UK Government has no credible way forward and urged May to allow another EU referendum to take place.

"I think if we were in any normal period in British politics, she would be long gone, but the conventional rules are not applying," said Sturgeon.

"I suppose the one caveat to that is I think she is effectively out of power now and perhaps debating her position is becoming more and more incidental by the day.

"The Government has absolutely failed to deliver on the result of the 2016 referendum.

"They have no credible way forward now and when Parliament and Government fails, then it seems to me the only sensible thing to do is put the people back in charge."

Sturgeon joined politicians and campaigners in London on Saturday in calling for a public vote on EU membership.

Around one million people are believed to have participated in a march at the event, which finished with a rally at Parliament Square.

The First Minister said that the SNP's first choice would be to remain within the EU, rather than having a "soft" Brexit, indicating that such an option would still be possible.

"Our first preference is to remain and the best way of achieving that is to have another referendum or to revoke Article 50," she said.

"At the moment, I think it's fair to say that the option of remaining is not off the table and it's not beyond the realms of possibility by any stretch of imagination.

"So as long as our first preference remains an option, that is what the SNP will back."

The First Minister has previously indicated that she would set out a timetable for holding a second referendum on Scottish independence when there is greater clarity on Brexit, and told Andrew Marr that the case for independence had been bolstered by events of the past three years.

"I think another Scottish independence referendum is going to happen," said Sturgeon.

"Nothing in this life is absolutely inevitable, but I think it's as inevitable as it's possible to be.

"Before I set a path forward for Scotland, I think it's reasonable for me to know what the starting point of that journey is going to be and the context in which we are going to be embarking on it.

"We need to know and hopefully we will know this over the next few days and the next three weeks - is the UK leaving the EU? Is it leaving with a deal? Is it leaving with no deal or is it not leaving at all? Perhaps looking at another referendum.

"But the experience of the last almost three years now - Scotland's vote ignored, the voice of the Scottish Parliament ignored, all of the consequences that flow from Brexit completely outwith our control - that really does make the case for independence very, very powerfully."

Sturgeon added that she was in favour of Scotland entering the EU in the event of independence and said the country should not have to choose between access to the UK and European markets.

"I would want to see an independent Scotland rejoin the EU," said Sturgeon.

"One of the big ironies is that in the independence referendum, those who were against Scottish independence said: 'You can't have independence because you'll get thrown out of the EU'.

"What an irony that not too much further on, we're facing being taken out against our will."

The Scottish Conservatives' constitution spokesman Adam Tomkins said: "Nicola Sturgeon's visit to London was a scam. She wasn't there because she cares about the UK leaving the EU or to try and influence proceedings in the coming days.

"She was there to agitate for a second independence referendum, and to set Scotland up for even more years of division.

"Independence is the only thing on her radar. Her obsession is stopping Scotland from getting on and doing the things that really matter to people."