Two people who were searched under the Terrorism Act as they prepared to visit an arms fair have asked the lord chief justice to declare the action unlawful.
Police have search powers under the Terrorism Act 2000.
Student Kevin Gillan and journalist Pennie Quinton were searched as they neared Europe's largest arms fair last September in London's Docklands.
Since February 2001, the Home Secretary can authorise the Metropolitan Police to make random searches.
However, the pair's lawyer has argued that such ongoing powers are unlawful.
Rabinder Singh QC told Lord Woolf, Lord Justice Buxton and Lady Justice Arden on Monday that
the random searches were a "recipe for the arbitrary use of power".
The appeal is backed by campaign group Liberty, who advised the pair that the Metropolitan assistant commissioner had applied for the powers under Section 44 of the Terrorism Act and these were authorised in secret by Home Secretary David Blunkett, Mr Singh told the judges.
The first authorisations began when the Terrorism Act came into force in February 2001 - more than six months before the 11 September terrorist atrocities in the United States - and have been continued ever since.
"In short, the people of London have been continuously subject to emergency stop and search powers for the last two years and nine months," said Mr Singh.
He added that while thousands of people had been searched by the Metropolitan Police, there was no evidence to show any had been held for a terrorist offence.
"The only reasonable conclusion to draw is that Metropolitan police officers
are using their powers under Section 44 authorisations as an additional tool in
their day-to-day policing kit..."
As this could never have been the intention of Parliament, Mr Singh said, the making and authorising of the powers was unlawful.
"The legislation specifically provides the officer does not have to have
reasonable grounds to suspect.
"We say in essence this is a recipe for the
arbitrary use of power."
Mr Gillan, 26, from Sheffield, was in the area to join a peaceful protest and Ms Quinton, 32, from Bermondsey, south east London, was on her way to film the protests.
High Court failure
Their cases have already been rejected by the High Court.
In October, the High Court judges said the use of the random stop-and-search powers and any resulting violation of human rights was justified in the light of the threat of terrorism.
But the judges gave the civil rights campaigners permission to appeal against their decision to the Court of Appeal because a matter of wide public importance had been raised.
Liberty said they have been approached by more than 50 people concerning police conduct at the arms fair.
Scotland Yard said it does not have any figures on how many people were searched but said a total of 154 were arrested.