Lord Garnier QC is now setting out the arguments made in Sir John Major's submissions.

He says it argues there is no reason for proroguing Parliament for five weeks, "let alone five critical weeks in a period in which time is of the essence".

Lord Garnier says Sir John Major also identifies evidence that the decision to prorogue was "motivated by a desire to prevent Parliament interfering with the prime minister's policies during that period".

Mr Fordham has finished his submission to the court.

Next up: an oral intervention by Lord Garnier QC, speaking on behalf of former Conservative prime minister Sir John Major.

Image source, PA Media

Meanwhile, the UK government says it has shared its Brexit ideas with the EU.

It said these ideas had been reflected in a "series of confidential technical non-papers".

But Downing Street says it will submit formal written solutions "when we are ready" rather than meeting an "artificial deadline".

A spokeswoman said it followed "detailed discussions with the commission's taskforce" in recent weeks.

"We have now shared in written form a series of confidential technical non-papers which reflect the ideas the UK has been putting forward.

The EU confirmed it had received the documents and added that "technical discussions... on some aspects of customs, manufactured goods and sanitary and phytosanitary rules" would take place today and tomorrow.

The EU's chief negotiatior, Michel Barnier, is set to meet Brexit Secretary Steve Barclay on Friday.

Read the full story here,

Mike Fordham QC has been referring to the government's written submission to the Supreme Court on what it should order the prime minsiter to do, were it to rule against Boris Johnson - but this has not been made public.

In his written submissions, Mr Fordham QC told the justices that PM's decision to prorogue parliament for up to almost five weeks had "consciously and purposely impeded the constitutional principle of parliamentary sovereignty".

He said Boris Johnson's decision had "impeded the ability of the National Assembly for Wales to engage in dialogue with the Westminster Parliament" at an important time, with the UK considering how it would leave the EU.

Mr Lavery has finished his submission to the court.

Next up is an oral Intervention by Counsel General for Wales, Mike Fordham QC - the Welsh government's chief legal adviser.

Dominic Casciani
Home Affairs Correspondent

Mr Lavery finding it tough going with some justices, in particular Lord Reed.

He's asked whether prorogation has a really specific impact on Northern Ireland that opens up a legal question they need to grapple with - or whether the submissions are merely a complaint about Brexit.

Image source, AFP/Getty Images

Brexit Secretary Stephen Barclay has been addressing business people and members of the press in Madrid, where he is meeting European counterparts.

Asked about the Supreme Court case he says:

"The UK government will abide by the law. The ministerial code requires ministers, including myself, to abide by the law and of course we will abide by the law.

"That is not to say we will look at it closely and test exactly where we are, but the best way to address this is through a deal."

Mr Lavery says the Yellowhammer report shows that "calamity" will befall Northern Ireland in the wake of a no-deal Brexit,

But one of the judges says the effects of how the UK leaves the EU are "completely irrelevant to the legal questions" they are faced with in the case.

Mr Lavery argues that the "context" of Brexit is important to justiciability - which is whether prorogation is a matter for the courts, or a political matter.

And he says Parliament will not be able to prevent potential difficulties outlined by the Yellowhammer report if it's not sitting.

Mr Lavery tells the court the impact of prorogation is not just the loss of parliamentary scrutiny but, at a Northern Ireland level, nobody can be appointed to run public buses.

However, Lady Hale says the court is not concerned with Brexit and its implications but with the lawfulness of the decision to prorogue Parliament for five weeks.

Mr Lavery says the judges should intervene if they consider prorogation was designed to "run down the clock" towards a no-deal Brexit.

Mr Lavery, representing Northern Ireland victims' campaigner Raymond McCord, says it is important to understand the role of the EU as a "peace project".

It's enabled close co-operation between the UK and the Republic of Ireland, he says.

He is urging the court to look at this legal question in the way it impacts Northern Ireland in particular.

Dominic Casciani
Home Affairs Correspondent

The government has made written submissions to the Supreme Court on what it should order the prime minister to do, were it to rule against Boris Johnson,

This is critical to understanding how and when Parliament can return.

But we can’t tell you what it says – it’s not been disclosed.

The Attorney General’s Office has told the media that it is not being published unless we force it to be released by order of the court.

Raymond McCord's 22-year-old son Raymond junior, was murdered by the UVF in Belfast in 1997.

No one has ever been convicted of the former RAF man's murder.

Mr McCord brought separate proceedings in Belfast, arguing that a no-deal Brexit would damage the Northern Ireland peace process