London, England (CNN) The UK Government does not plan to trigger Article 50 of the Lisbon treaty initiating the UK's departure from the European Union before the end of this year, the country's High Court was told Tuesday.

The British position was revealed at the opening of the first legal challenge to the Brexit process.

Lead claimant Gina Miller, founder of London-based investment group SCM Private, is arguing that neither the UK government nor the prime minister can trigger Article 50, which would kick off negotiations over the UK's exit, alone.

"We will be making the argument that the correct constitutional process of parliamentary scrutiny and approval as well as consultation with the devolved administration in Scotland and Northern Ireland and the Welsh Assembly needs to be followed," Miller told CNN. "Otherwise the notice to withdraw from the European Union would be unlawful and subject to legal challenge."

The matter will now be heard by the High Court in October.

New Prime Minister Theresa May is already facing opposition from the Scottish Nationalist Party, which is against Brexit. Scotland voted overwhelmingly to remain during last month's referendum.

May is pictured at her first Cabinet meeting Tuesday.

The new UK Prime Minister Theresa May is already facing opposition from the Scottish Nationalist Party which is against Brexit. Scotland voted overwhelmingly to remain during last month's referendum.

Following May's meeting last week with Scottish First Minister Nicola Sturgeon she told British media : "I won't be triggering Article 50 until I think we have a UK approach and objectives for negotiations."

The court case comes a day after May was challenged by a Scottish Nationalist MP over her stance on renewing the UK's nuclear deterrent.

May stated bluntly that she would authorize a nuclear strike that could kill thousands as she outlined the case for replacing the UK's submarines that carry Trident nuclear missiles.

May was asked by George Kerevan if she was "personally prepared to authorize a nuclear strike that could kill 100,000 innocent men, women and children?"

May replied: "Yes. The whole point of a deterrent is that our enemies need to know that we would be prepared to use it."

The PM's declaration came during a parliamentary debate in which she warned it would be a "reckless gamble" for the UK to rely on other nations for its nuclear deterrent.

The debate was her first as prime minister. The Commons voted overwhelmingly by 472 votes to 117 to replace the aging Vanguard submarine fleet with four new vessels.

The vote was not technically necessary, and commentators noted that it seemed to have been staged by the government for the purpose of highlighting the rift between Labour leader Jeremy Corbyn and a majority of Labour MPs.

May launched an attack on Corbyn by claiming some Opposition frontbenchers appeared to be the first to "defend the country's enemies" and the last to accept what the UK needs to protect itself.

Labour is split three ways with the majority of the party's MPs voting in favor of renewing the Trident system -- in line with the Opposition's official policy -- while others abstained or, like Corbyn, opposed the motion.

The Labour leader repeated his position that he would not be prepared to press the nuclear button if he was prime minister, arguing that threatening "mass murder" was not the way to handle international relations.

A series of his own MPs lined up to challenge him over his support for unilateral disarmament in the latest sign of discontent over his leadership.

CNN politics expert Robin Oakley said: "The Trident debate, already planned by David Cameron before he resigned, was not strictly necessary to the continuance of the program. That had been agreed back in 2007. But the Conservative government saw it as a rallying point after the Brexit vote and a chance to highlight the Opposition Labour Party's deep divisions."

Reflecting on May's first performance at the despatch box, Julian Brazier, a Conservative MP with a particular interest in military and defense issues in the House of Commons, told CNN: "She means what she says. This is exactly the sort of firm, clear, direct leadership that the party needs. I am delighted to see it."

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May has held her first Cabinet meeting since becoming prime minister on July 13. She has already demonstrated her authority by carrying out one of the most extensive Cabinet reshuffles . Only five of the 22 members of her Cabinet occupy the same positions they did under David Cameron.

In Tuesday's meeting she heard from new Chancellor Philip Hammond and new Foreign Secretary Boris Johnson.

On Wednesday, May, the former Home Secretary, will make her debut as prime minister on the international stage, meeting German Chancellor Angela Merkel in Berlin.

On Thursday she will hold talks with French President Francois Hollande in Paris. Britain's exit from the European Union is set to be on the agenda at both meetings.