Supreme Court judges are "struggling" to see how a mechanism ensuring Holyrood must give its consent to changes to its competence is relevant to the Brexit case, judge Lord Wilson has said.

The judge made the remark on third day of the four-day hearing in London, where the Scottish Government's top lawyer James Wolffe was appearing before the court.

In his written submission to the court, the lord advocate argues the Sewel convention, the understanding that Holyrood must give its consent to Westminster altering its powers, was required as withdrawing from the EU will "change the legislative competence of the Scottish Parliament".

The UK Government is appealing to the court to overturn an earlier verdict by the High Court which ruled the Prime Minister cannot trigger Article 50 without the prior consent of MPs.

Lord Wilson said: "Mr Wolffe, I think many of us are struggling to see exactly how the Sewel convention impacts on the central issue before us.

"Are you saying simply the impact is this 'if unto the extent that Sewel convention would politically oblige parliament to consult the Scottish Parliament before triggering Article 50?'

"That is an extra argument for why parliament or the executive or does it fit in for another way?"

Mr Wolffe told the court he was not pursuing a "veto" over the UK's exit from the EU but instead over its "effects" on the devolved administration.

He said: "Can I make clear that I do not assert that the Scottish Parliament has a veto on the decision to withdraw the United Kingdom from the European Union?

"That decision is ultimately, I say, for the Queen in parliament.

"What I do say is that the question whether the Scottish Parliament consents or does not consent to the effects of withdrawal, with regards to devolved matters, is by virtue of the legislative consent convention a matter of constitutional significance."

Mr Wolffe added he was inviting the court to agree with him to uphold the "proper institutional roles" of Westminster and the Scottish Parliament.

Supreme Court president Lord Neuberger also questioned the relevance of the Sewell convention to the case.

He asked: "If the UK Parliament does breach this convention what is the argument?

"We would be entitled nonetheless to stop the UK Parliament doing it if it was proposing to?

"I suppose the further question is what the relevance of this? We are not talking about the UK Parliament legislating we are talking about a case where it is proposing to use its executive powers."

The lord advocate responded to question by telling Lord Neuberger he must "keep in mind" that in "the current constitutional arrangements there are several legislatures with an interest" on the question if the UK Government can change the "law of the land" through its use of executive power .

Mr Wolffe will return to the Supreme Court on Friday to put forward his final submission to the justices.