Brexit has highlighted “real weaknesses” in the UK’s devolution settlement, Nicola Sturgeon said, as she again urged Tory leaders to consider keeping the whole UK in the single market.

She spoke out after “frank” exchanges with Cabinet Office Minister David Lidington on the differences between the Scottish and UK governments over their approach to exiting the European Union (EU).

The First Minister was speaking following a meeting of the British-Irish Council on the Isle of Man, which was also attended by Welsh First Minister Carwyn Jones and Ireland’s Leo Varadkar.

She said: “I will make no bones about the fact that the Brexit experience has exposed real weaknesses within the devolution settlement that will require them to be worked through and resolved along the way.

“There have been frustrations on the part of the Scottish Government about lack of engagement and involvement – obviously we’ve had quite heated debates and discussions around power grabs on the devolved parliaments and issues around how the power of the devolved administrations are respected.”

She added: “There’s no point in not being up front and frank about that, and it’s something David and I, and Carwyn Jones, touched on this morning that we need to make sure that we are recognising that and thinking how we resolve these issues in future.”

“In some ways, perhaps, those issues have actually strengthened the Scotland-Wales relationship over the last couple of years and that has huge benefits for a whole range of reasons.

“Similarly, I don’t think the relationship between Scotland and Ireland has ever been stronger than it is at the moment. It’s an incredibly good relationship that has huge economic, social and cultural benefits for both of our countries.

“Around the British and Irish Council table I detect nothing but strong desire to ensure that whatever happens in Brexit, we are all working to make sure that these relationships continue to be as strong as they are.”

Ms Sturgeon also said that if a deal proposed by the UK Government cannot command a majority in the House of Commons, it should not mean that departing the EU with no deal is “inevitable”.

The First Minister has previously stated that she would not vote for any deal that does not keep UK within the single market and the customs union.

It follows a vote on Holyrood on Wednesday that saw a majority of MSPs express their “unequivocal support” for a referendum on the final terms of Brexit.

She said: “My preferred option all along, if the UK is leaving the EU, which I regret, is that it should seek to stay in the single market and the customs union, which would resolve along the way the issues around it, with the Northern Ireland/Republic border and the border between Ireland and Great Britain.”