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A British Muslim couple were jailed for glorifying the murder of Fusilier Lee Rigby by posting videos on YouTube that were "offensive in the extreme".

Royal Barnes, 23, and his wife Rebekah Dawson, 22, recorded and uploaded three videos shortly after the murder in Woolwich, south east London, last May.

Barnes, of Hackney, east London was jailed for five years and four months at the Old Bailey after pleading guilty last month to three counts of disseminating a terrorist publication and one of inciting murder.

His wife, who insisted on wearing her veil in court, admitted charges of disseminating a terrorist publication and was sentenced to 20 months in prison.

Judge Brian Barker QC told them the videos they made were "offensive in the extreme".

He said the couple showed "a total and continuing disregard" for how their actions might affect the family of trooper Rigby, those people who witnessed the murder and the British public.

In one seven-minute video, Barnes hailed the murder as a "brilliant day", while in another posted under his account Musa Real Talks he mocked the outpouring of public grief.

The footage showed him laughing uncontrollably as he drove past floral tributes.

A third video shows Dawson in a face veil behind a title: "British troops kill Muslims so they will die on London streets."

In it, she says: "Obviously now this guy who has been killed, Joe Blogg's or whatever his name is, was killed, this is the lion, the tiger fighting back...We are fighting back and Sharia, obviously the Islamic law, will dominate the entire world....don't worry, it is coming Inshallah (God willing)."

The first and second films were only on YouTube for two to three days, while the third remained online for two weeks. Only the first video was removed by YouTube itself.

Barnes, who knew murderer Michael Adebowale, also posted on Facebook the offer of a reward for avenging the rape of an Iraqi woman. None of his 500 friends replied.

(Image: Met Police)

The post on June 12, 2013, stated: "Any1 who kills an invading soldier in Muslim land I will give them a Vauxhall Astra 3door and money (French British American any kaffir soldier take ur pick)."

Prosecutor Kate Wilkinson told the court that before the postings, Barnes had been involved with a Sharia Law patrol of London streets, ordering women in short skirts to cover up and telling people to stop drinking alcohol.

He was also a member of extremist group Al-Muhajiroun - or Muslims Against Crusades - taking part in demonstrations advocating Sharia Law in the UK, including one on December 24, 2012, outside St Paul's Cathedral with Adebowale.

Another video clip retrieved by police showed Barnes at Finsbury Park Tube station pretending to be a suicide bomber on the platform in front of other passengers.

A further video of Barnes secretly filmed in the dock at Westminster Magistrates' Court showed him being sentenced for a public order offence after an English Defence League demonstration, before mocking British justice and bragging he is "free as a bird".

The last video shown in court was of a vigilante-style Sharia Muslim patrol in east London.

Barnes covers his face in a scarf to rant about Sharia Law on the streets before a clip of a drunken man falling asleep at a bus stop with sound effects of guns being cocked.

Temporary Commander Duncan Ball, head of the Counter Terrorism Command, welcomed today's outcome.

He said: "Disseminating violent extremist material and encouraging others to carry out acts of terrorism are serious offences and I hope today's sentences send out a clear message that we will arrest and prosecute those responsible."

Michael Adebolajo, 29, was sentenced to a whole life prison term while Michael Adebowale, 22, got at least 45 years for the murder of Lee Rigby last month.

The British Muslim converts ran the soldier down in a car before hacking him to death with a meat cleaver and knives in a frenzied attack last spring. They dumped his body in the middle of the road near Woolwich Barracks.