Updated

British judges have tossed out appeals by the Al Qaeda-inspired killers of a British soldier, saying their tough sentences were just punishment for the "horrific and barbaric" murder.

Three appeals court judges led by Lord Chief Justice John Thomas said Wednesday that Michael Adebolajo could not try to overturn his conviction, and neither he nor accomplice Michael Adebowale could seek reduced prison terms.

Adebolajo was sentenced to life without parole and Adebowale to a minimum of 45 years for the frenzied attack on Fusilier Lee Rigby in May 2013.

Adebolajo, a self-styled "soldier of Allah," appealed on the grounds that he was engaged in a war. Thomas called the attempt to challenge his conviction "completely hopeless."

Members of Rigby's family broke down in tears during Wednesday's hearing as the attack was described in court.