Two British-born, al-Qaida-inspired extremists who considered themselves "soldiers of Allah" were convicted Thursday of murdering an off-duty serviceman who was run down with a car and stabbed to death in a frenzied attack on a London street.

LONDON -- Two Islamic extremists were found guilty Thursday of the murder of a young British soldier whom they knocked down with a car and then hacked to death on a London street in full view of horrified bystanders.

A jury took less than two hours to convict Michael Adebolajo and Michael Adebowale in the brutal May 22 killing of machine gunner and drummer Lee Rigby as he returned to his barracks in southeast London. The incident was the first fatal Islamic terrorist attack on British soil since the multiple bombings on London’s transport network in 2005.

The two men were acquitted of the attempted murder of a police officer who responded to the attack. Prison sentences in the case are to be handed down in the coming weeks.

During their trial, the two described themselves as soldiers of Allah and Rigby’s slaying as a justifiable act of war as a result of British foreign policy in nations such as Iraq and Afghanistan. Adebolajo was caught on video by a witness immediately after the attack, holding a bloody cleaver and ranting that the killing was retribution for the deaths of Muslim women and children.

“You people will never be safe!” he shouted at passersby. “Remove your government! They don’t care about you.”

Both Adebolajo, who was 28 at the time of the attack, and Adebowale, who was 22, are British citizens of Nigerian descent. Adebolajo had converted to Islam from Christianity and had grown increasingly radical in his beliefs, investigators have said.

Though they professed support for Al Qaeda -- “they’re my brothers,” Adebolajo said in court -- the two men are not believed to have any formal involvement with the group.

The savage assault raised fears of more “lone wolf” attacks by religious extremists operating below the radar of intelligence agencies. The government has launched an investigation into whether the Internet and institutions such as prisons, universities and Muslim charities have become a “conveyor belt” of Islamist radicalization.

“We have to redouble our efforts to confront the poisonous narrative of extremism and violence that lay behind these [attacks] and make sure that we do everything to beat it in our country,” Prime Minister David Cameron told reporters after the verdicts were returned.

Jurors heard harrowing accounts from prosecution witnesses and from the attackers themselves concerning the assault on Rigby, who was returning to his barracks after a shift at the Tower of London. Adebolajo, the more outspoken of the two defendants, testified that they lay in wait for a British soldier to cross their paths and that Rigby happened to be the first.

They identified him from the military backpack he had slung over his shoulder, he said.

Video showed them ramming their car into Rigby, who was thrown into the air. Adebolajo then set to butchering him on the ground, attempting to decapitate him with a huge knife, and Adebowale soon joined in.

When police arrived, the two were armed with at least one gun. Officers shot both men and arrested them.

Sue Hemming, the head of the counter-terrorism division of the Crown Prosecution Service, said Thursday that the attack was “one of the most savage offenses prosecuted by our counter-terrorism lawyers.”

Rigby was married and had a young son.

“This has been the toughest time of our lives," his family said in a statement. "No one should have to go through what we’ve been through as a family. We are satisfied that justice has been done. But unfortunately, no amount of justice will bring Lee back.”

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Twitter: @HenryHChu

henry.chu@latimes.com