Abdulla Ahmed Ali, 27, Assad Sarwar, 28, and Tanvir Hussain, 27, admitted the offence at Woolwich Crown Court, in south east London.
The men also admitted conspiring to cause public nuisance by distributing videos threatening suicide bomb attacks in Britain.
Two of their co-defendants, Ibrahim Savant, 27, and Umar Islam, 30, also admitted conspiring to cause a public nuisance.
A jury must still decide if the five men, and three others, are guilty of conspiring to murder thousands in a wave of mid-air terrorist explosions using homemade liquid bombs.
They were being assembled at a bomb factory flat bought by the gang for cash in Forest Road, Walthamstow, north east London, the court heard.
The same flat was used by six members of the gang to record martyrdom videos in which they ranted hatred against the West and non-Muslims, jurors were told.
He said Ali, the alleged ringleader of the plot, was caught with a blueprint for the operation recorded in a pocket diary and on a computer memory stick.
Stashes of hydrogen peroxide and other bomb-making equipment were found hidden at Sarwar’s home and in woodland nearby, the court heard.
In their defence, Ali and Sarwar said they planned to record a documentary highlighting injustices against Muslims in Iraq, Afghanistan and Lebanon.
A small explosion at the Houses of Parliament in which no one would be hurt would act as a publicity stunt to draw attention to the programme.
The two men also considered other targets including gas terminals, oil refineries and airports, Sarwar said.
Ali and the five other men who recorded videos said they were acting the role of violent hate-filled extremists and the footage would be woven into the video.