Mohibur Rahman, Khobaib Hussain and Naweed Ali were part of a terror cell which was busted after British spies bugged Ali's car and found a pipe bomb and meat cleaver hidden in a sports bag in England's West Midlands region in August 2016.
The fourth member of the gang was 38-year-old Tahir Aziz.
The four, aged between 25 and 38, were convicted after a 23-week trial at the Old Bailey court in London yesterday.
He agreed with prosecution lawyer that the defendants may have planned to use their cars as weapons after being influenced by Islamic State's Nice attack last year that left 86 victims dead.
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"These attacks demonstrate in stark form the carnage that can be created by different types of terrorist attack that can be carried out with a vehicle, explosives and loaded weapons."
The gang were poised to strike police and military targets in the UK using a pipe bomb and meat cleaver inscribed with an Arabic word meaning "disbeliever".
The trio refused to leave the high-security Belmarsh Prison in London to attend the sentencing hearing today.
The judge handed down the trio a minimum term of 20 years for their "significant role" in the planned attack.
Aziz, who became involved in the plot at a later stage, was ordered to serve a minimum term of 15 years.
The suspects had claimed in court that the evidence was planted by an undercover officer, but they were unanimously found guilty by a jury yesterday.
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