Two people have launched a High Court damages claim against the Met for allegedly detaining them for more than six hours during May Day protests.
Civil liberties groups accused the police of heavy-handedness
Protester Lois Austin and passer-by Geoffrey Saxby said they were among thousands of protesters held by riot police in central London in 2001.
The pair claim the police's tactics breached the Human Rights Act.
The test case is important as it raises questions over the police's power to control demonstrations.
Ms Austin said she was taking part in the demonstration but needed to leave at 1600 GMT to collect her 11-month-old baby from a crèche.
But she said she was not allowed to do so, and had to ask a friend to collect the baby.
Mr Saxby said he was not involved in the protest, but was caught up in the chaos while collecting money from a bank on behalf of his employer.
Distress and alarm
Both are claiming damages against the Metropolitan Police, alleging false imprisonment and breach of their human rights.
They claim that the police action in detaining them at Oxford Circus caused them distress and alarm and left them feeling humiliated and intimidated.
The case is supported by human rights organisation Liberty.
Their counsel, Keir Starmer QC, told the court on Monday: "Our broad position is that there is no power to detain those who are not presenting any danger to the peace.
The police contest the claims and are expected to call a large number of witnesses, including the Mayor of London, Ken Livingstone.