A major terrorism hearing is taking place at the Old Bailey amid a bid from prosecutors to ban press and public from proceedings.
They also want to grant the two defendants anonymity and only allow reporting of some of the charges.
The Sunday Times reported yesterday that the application is being called for by Scotland Yard for “strong operational reasons”.
The paper reports that the two men facing trial, both aged 25, were arrested last month on the outskirts of the City of London.
They have been identified only as AB and CD and are said to be British citizens, one of Turkish origin and the other with an Algerian background.
AB is said to have been charged with the preparation of terrorist acts, and both are charged with collecting or recording information likely to be useful for a terrorism act.
Meanwhile the two men accused of murdering soldier Lee Rigby were due to appear at a pre-trial hearing today at the Old Bailey.
Michael Adebolajo, 28, and Michael Adebowale, 22, are charged with murdering the Fusilier as he walked back to Woolwich Barracks in south-east London on 22 May.
They are also each accused of attempting to murder a police officer on the same day, and conspiracy to murder a police officer on or before that day.
Far-right protesters are expected to gathered outside the court this morning.