Individuals arrested or subjected to police searches are challenging the legality of the policing of the royal wedding in London last year.
As another major royal event fast approaches, the police are being accused of operating an unlawful policy of arresting those with "anti-monarchist" views.
The challenge is being heard by Lord Justice Richards and Mr Justice Openshaw sitting at the High Court in London.
Metropolitan Police lawyers are expected to argue there is no evidence that an unlawful policy was in operation on Friday April 29, 2011 when Prince William married Kate Middleton.
The application for judicial review is being brought by some 20 individuals who were arrested on the wedding day, or were subjected to searches on days leading up to it.