Richard Dart, 30; Jahangir Alom, 26; and Imran Mahmood, 21, entered their pleas in London during a hearing, the BBC reported.
Prosecutors said the trio had prepared for acts of terrorism by traveling to Pakistan for training from July 2010 and July 2012 and had provided information to others about how to go to Pakistan for the same purpose.
Alom used to be a police community support officer.
Dart, a recent convert to Islam, had taken the name Salahuddin al-Britani. His conversion was documented in a BBC show filmed by his stepbrother.
No evidence was presented in court about how the men were recruited to commit terrorist attacks.
Anjem Choudary, the man who converted Dart to Islam, denied any involvement in convincing Dart and the others to commit acts of terrorism.
"If someone is doing anything like that -- and I don't think Salahuddin and Jahangir are, by the way -- they are doing it behind the scenes. They are not doing it from encouragement by us."
Choudary was the leader of Muslims Against Crusade before it was banned by the British government in November 2011 as a terrorist organization.