Boris Johnson is secretly pursuing a “dangerous” no-deal Brexit, Nicola Sturgeon said after her first meeting with the new Prime Minister.

She warned it was now “almost inevitable” the UK will leave the European Union without a deal, despite Johnson insisting an agreement can be reached with Brussels.

Johnson, who was booed by protesters as he entered the Scottish first minister’s official residence in Edinburgh, said there was a “very good chance we can get a deal”.

The PM accepted there was “no change” in the position of EU leaders – who have been consistent that they will not renegotiate the Withdrawal Agreement reached by Theresa May.

Despite that he insisted: “There is ample scope to do a new deal, to do a new deal and a better deal.”

But Sturgeon said: “After my discussions with Boris Johnson, behind all of the bluff and bluster, this is a government that is dangerous.

“I think the path that it is pursuing is a dangerous one for Scotland and for all of the UK.

“He says publicly – and he said it to me again today – that he wants a deal with the EU, but there is no clarity whatsoever about how he thinks he can get from the position now where he’s taking a very hard line – the withdrawal agreement is dead, the backstop is dead.

“If I listen to all of that and listen to what’s not being said as well as what is being said, I think that this is a government that is pursuing a no-deal strategy, however much they may deny that in public.”

The SNP leader added: “I think, if he were in this room right now, he would deny this vehemently, but I think he wants a no-deal Brexit.”

She spoke out as Johnson made his first visit to Scotland since becoming Prime Minister, starting with a tour round the HMS Victorious nuclear submarine on the Faslane naval base on the Clyde.

He then went on to have meetings in Edinburgh with Scottish Tory leader Ruth Davidson – who has made plain her opposition to a no-deal Brexit – as well as the First Minister.

After his meeting with Sturgeon, Johnson left Bute House by the back door.

The new PM used his visit to insist there is “no reason” for Scots to have the second independence referendum that Sturgeon is pushing for.

He hit out at the “campaign to destroy the union” from the SNP – and while he refused to unequivocally rule out granting Holyrood permission for a second independence referendum, he said comments that the 2014 ballot was a “once in a generation” event must be respected.

A Number 10 spokesman said: “On Brexit, the Prime Minister said that while the government’s preference is to negotiate a new deal which abolishes the anti-democratic backstop, the UK will be leaving the EU on October 31 come what may.”

Johnson said while he was “aiming for a new deal” with Brussels, it was government policy to prepare for a no-deal outcome.

“That is what we are going to do with high hearts and growing confidence, we will prepare for a no-deal Brexit.”