A British Muslim couple were jailed today for glorifying the murder of Fusilier Lee Rigby in videos posted 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 last May.

Barnes 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.

Barnes, 23, and Dawson 22, of Hackney, north east London, embraced in the dock and insisted they would not be separated by a security guard at the start of the hearing.

Before sentencing, the judge asked Dawson's lawyer to confirm the defendant was the woman in the dock in the full veil.

The court heard the first of the three videos was made on the day Fusilier Rigby was murdered, with Barnes hailing it as a "brilliant" day.

It was edited with graphic images of a man holding a decapitated head, a scene of the Woolwich murder and the Twin Towers, and sent on YouTube the following day.

The second video contained the same edited images and saw Dawson ranting about how British troops would be killed on the streets of London.

Then in a follow-up, Barnes mocked the outpouring of public grief, laughing uncontrollably as he drove past floral tributes with Dawson.

Prosecutor Kate Wilkinson said Dawson sent links of the videos to contacts and friends and received some negative comments back.

One friend said to her: "Can you please stop sending me these links. I'm not interested in it."

Another told Dawson: "Be careful with the YouTube stuff."

Dawson replied: "My husband took this one down. If they got that they would have arrested. Have you watched it - it was really inciting and almost glorifying. LOL."

Dawson called her husband "Babes" in messages between them discussing the videos. In one, she told Barnes: "Babes, someone has reported the laughing video. It has been removed."

Barnes, who knew one of the murderers, 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.

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).''

Michael Adebolajo, 29, was given a whole-life term and Adebowale, 22, was sentenced to life with a minimum term of 45 years at a hearing last month after being found guilty of Fusilier Rigby's murder.

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. They dumped his body in the middle of the road near Woolwich Barracks.

Dawson has no previous convictions, apart from a charge of witness intimidation that she has admitted and is awaiting sentence for, the court was told.

But Barnes has a string of convictions for using threatening words or behaviour, and one for assault on a security guard at a mosque. He also has a five-year anti-social behaviour order (Asbo) for taking part in vigilante patrols of east London promoting Sharia law, the court was told.

Mitigating for Barnes, Naeem Mian told the court: "There are no ifs, no buts, no maybes, Mr Barnes makes it absolutely clear that these are idiotic acts borne out of breathtaking stupidity."

He said his client was vulnerable to coming under bad influences, having been taken into care at the age of eight and prevented from attending his mother's funeral after she died in custody.

Dawson's lawyer Susan Meek said her client, who had been studying at university, also came under the influence of others and her dreams of becoming a teacher were now in tatters.

She said: "Over the last nine months, her faith and dress has been put under national and international limelight and it has caused her to reflect deeply about her belief and the way she lives her life and her religion.

"There is an understanding from her all she wants now is to live a life quietly, legally, as a wife to her husband and have a family."

The judge, who is Recorder of London, sentenced Barnes to 26 months in jail for each of the three counts relating to the YouTube videos.

Mr Barker said the charge of inciting murder was more serious because it "encouraged others to carry on the war against the West" and kill soldiers.

For this, he handed Barnes five years and four months' imprisonment, all to run concurrently.

Dawson was sentenced to 20 months' imprisonment for each of the first three charges, to run concurrently.

Mr Barker told the couple: "Freedom of speech has long been jealously regarded by the law but with that freedom comes respect and responsibility."

Mari Reid, of the Crown Prosecution Service's Counter Terrorism Division, said afterwards: "While the whole country was unified in grief and horror in the wake of Fusilier Lee Rigby's death last year, Royal Barnes and his wife sought to take advantage of the situation to promote their extremist views.

"Royal Barnes went further, using the savage attack on Fusilier Rigby to encourage others, via Facebook, to murder British, French and American soldiers.

"These were not throwaway comments from a thoughtless individual, but the hardened beliefs of an extremist.

"We pride ourselves in Britain on allowing the right to free speech to flourish. But the vile views posted online by Royal Barnes and Rebekah Dawson justified and glorified terrorist attacks, and tried to foster hatred in our communities."

Temporary Commander Duncan Ball, head of the Counter Terrorism Command (SO15), 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."