The IndyCamp group set up a collection of caravans and tents outside Holyrood towards the end of 2015 and vowed to stay there until Scotland became independent.
It kickstarted a court battle as the Scottish Parliamentary Corporate Body (SPCB) sought to remove them from the grounds.
Judges at the Court of Session in Edinburgh ruled in favour of the parliament last summer, and again later on after an appeal, paving the way for the eviction of the campaigners on November 4.
Despite being removed from the site, the IndyCamp group continued its legal battle against the earlier court rulings.
They returned to Scotland’s highest civil court on Tuesday to apply for permission to appeal to the UK Supreme Court.
Three Court of Session judges hearing the application - Lady Dorrian, Lord Menzies and Lord Glennie - did not grant the group permission to take their legal battle to London.
Speaking after the hearing, a spokesman for the Judicial Office for Scotland confirmed: “The Inner House of the Court of Session refused to grant permission to appeal as the court did not consider that the applications raised arguable points of law of general public importance which ought to be considered by the Supreme Court at this time.”
In civil cases where leave to appeal to the Supreme Court is refused, a party can still go on to apply directly to the London-based court for permission to appeal.
It is understood the campaigners have 28 days in which to lodge any such application.
The group had argued its removal was unfair and objected to being evicted before the Supreme Court question had been dealt with.
Earlier hearings in the case saw unusual arguments aired in court, including claims that Jesus Christ had given permission for the camp.
A Scottish Parliament spokeswoman said on Tuesday: “We welcome the Court of Session’s decision today that the protesters have no grounds for a further appeal to the Supreme Court.
“We hope the protesters will accept the court’s ruling so we can bring matters to a close.”