The legal campaigner Gina Miller has vowed to continue her “fight for democracy” after the high court in London ruled that Boris Johnson’s decision to prorogue parliament for five weeks was legal.

Three of the most senior judges in England and Wales dismissed her claim that the prime minister acted unlawfully in giving advice to the Queen to suspend parliament from next week at a time of momentous political upheaval.

The lord chief justice, Lord Burnett of Maldon, the master of the rolls, Sir Terence Etherton, and the president of the Queen’s bench division, Dame Victoria Sharp, granted permission for the case to be appealed to the supreme court.

They gave no reasons for their decision, which is likely to be released next week. Sir James Eadie QC, for the prime minister, had argued it was a purely political decision that should not be subject to challenge in the courts.

Earlier this week, a Scottish court turned down a similar legal challenge. In Edinburgh, the inner house of the court of session has reserved until next Wednesday a decision on an initial appeal over the the legality of Johnson’s prorogation advice. It has also delayed until the same day any ruling about granting an interdict, or injunction, temporarily preventing the government’s suspension of parliament.

A third claim seeking to overturn the prime minister’s decision to prorogue parliament until 14 October was being heard in Belfast on Friday.

All three claims are likely to go to appeal and will be combined for a joint hearing expected at the supreme court for three days starting on 17 September.

Prorogation has never lasted longer than three weeks in the past 40 years and in most cases was only for a week or less, the London court was told.

During Thursday’s hearing, Lord Pannick QC, representing Miller, described the prime minister’s decision as an “unlawful abuse of power”.

Speaking afterwards outside the Royal Courts of Justice, Miller said she was disappointed at the decision but would fight on.

“We are very disappointed with the judgment today. We feel strongly that parliamentary sovereignty is fundamental to the stability and future of our country and is therefore worth fighting to defend. As our politics becomes more chaotic on a daily basis, the more vital it is that parliament is sitting. We are therefore pleased that the judges have given permission to appeal to the supreme court on the grounds that our case has merit.

“All of us here today, my legal team who have worked tirelessly over the last few weeks and I, feel we have no other option but to appeal this judgment to the supreme court. An appeal ‘leapfrog’ date has been set for 17 September.

“Today we stood up for everyone – we stood up for future generations, we stood up for our representative democracy, and tried to stop those who would wreck our constitution.

“To give up now would be a dereliction of our responsibility to help protect our elected representatives – our eyes and ears that sit in Westminster – who protect our rights and give each of us a voice.

“It is not right that they should be bullied or shut down – especially at this most momentous of times in the history of our United Kingdom. My legal team and I will not give up the fight for democracy.”

In Belfast, lawyers for the victims’ campaigner Raymond McCord told the high court that a no-deal Brexit on 31 October would create chaos for Northern Ireland.

Ronan Lavery QC, appearing for McCord, praised the EU for its role in underpinning the peace process. “To leave without a withdrawal agreement would create chaos and economic misery and a real threat to the peace process in Northern Ireland – it would be madness.”

McCord’s son, also called Raymond, was murdered by loyalists from the Ulster Volunteer Force in North Belfast in 1997. He has repeatedly voiced concerns about the impact of Brexit on the peace process.

All-island cooperation deepened following the 1998 Good Friday agreement, which largely ended the conflict. Campaigners fear the creation of a hard Irish border after a “no deal” Brexit would provide an opportunity for dissident republicans to reignite paramilitary violence.

“Our very simple proposition is that, when you take this piece of legislation, nothing sanctioned or authorised the executive [government] to take the drastic step of leaving the EU without a deal,” Lavery said.

“The court can intervene when the prime minister seeks to act in a way which is oppressive to the people of Northern Ireland contrary to their constitutional position.”

The hearing continues.