Of the two men arrested on the street; a 27-year-old was arrested on suspicion of the preparation of terrorist acts.
All three suspects have been taken to a south London police station for questioning as detectives homes and businesses in Ilford.
Counter terrorism officers, backed up by armed colleagues, and arrested two men on the street in Ilford, east London, late on Wednesday, while a third was arrested at a house nearby, police said in a statement.
Three men have been arrested on suspicion of terror offences in east London following a series of raids involving armed police. The intended truck was smaller but similar to the one used in the Nice attack a year ago that killed 86 people and injured hundreds in the resort town in the south of France.
The operation took place overnight and searches are ongoing at the properties, the force said. Searches of the residential address in Ilford and a business address in Ilford are continuing.
A total of 21 people have been arrested so far in the investigation into the suicide bombing.
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The 29-year-old man was arrested in the early hours of Friday morning on suspicion of being involved in the commission, preparation or instigation of acts of terrorism. Twelve were released without charge and nine remain in custody.
Police have named the attackers - who were all shot dead - as Youssef Zaghba, a 22-year-old Moroccan-Italian man who lived in east London; Khuram Butt, 27, from Barking; and Rachid Redouane, 30, who also lived in Barking.
Butt, 27, was a British citizen born in Pakistan who was known to security services, while Italian authorities said they warned the United Kingdom that 22-year-old Zaghba was a "possible suspect".
Public anger has grown at how the men were able to carry out an attack despite alarms being raised to the authorities, particularly after police revealed the Manchester bomber Salman Abedi was also known to intelligence services.
"I am deeply shocked, saddened and numbed by the actions of my ex-partner who has killed and injured so many innocent people".
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