Omar Khan, Jewel Uddin, Mohammed Hasseen, Mohammed Saud, Zohaib Ahmed and Anzal Hussain had all admitted terrorism offences in April.
But the plotters arrived two hours after the EDL event had ended.
The men, who all lived in or near Birmingham, were caught by chance after a car being used by two of them, and carrying weapons, was stopped by police on the M1 after the rally and found to have no insurance.
Hasseen, Hussain and Saud were jailed for 18 years and nine months, with a five-year extension on licence.
Extended sentences, introduced in England and Wales last year, mean offenders serve at least two-thirds of their main sentence in custody. After release, they are on licence in the community for the rest of their sentence plus the extension part.