Each defendant played a different role in the plot. Lorry driver Brian Mulcahay was the inside man.
Mulcahay, 46, of Grosvenor Road, Westcliff-on-Sea, Chatwood, of Sawyers Grove, and Stanley Rose, 75, of Iver, Pilgrims Hatch, both of Brentwood, and David Gale, 55, of Hansells Mead, Harlow, and Gary Cummings, 51, of Anne Way, Ilford, all Essex, pleaded guilty.
John Corley, 53, of Tankerton Road, Whitstable, Kent, was found guilty after a trial.
A seventh man, Matthew Middleton, 42, of Crows Road, Epping, Essex, also pleaded guilty and will be sentenced at a later date.
The Faiers sisters had been due to give evidence at Corley's trial but were not called.
More top news
The prime minister was shouted at as she left the scene of the tragedy in which at least 79 people died.
Do you know a fundraiser with an inspirational story to tell? Find out how to nominate your ITV London Fundraiser of the Year 2017
The inaugural service left London Liverpool Street for Shenfield, Essex, on the existing TfL Rail route on Thursday morning.