Their statement comes as Prime Minister David Cameron said he is "completely appalled" by the guilty verdicts.
Australian-born Peter Greste, Canadian-Egyptian acting Cairo bureau chief Mohammed Fahmy, and Egyptian producer Baher Mohammed, were sentenced for charges relating to terrorism, having been arrested in December as part of a crackdown on Islamist supporters of ousted President Mohammed Morsi.
Before the sentencing yesterday, members of Mr Greste's family, including his brother Andrew, were in court. Shortly after the verdicts the family wrote on a Facebook page called 'Free Peter Greste'.
"We are so devastated!" they said. "Peter has received seven years. This is not the end. Please make noise, this is unjust and a slap in the face for freedom of speech and media."
Mr Greste left Australia in 1991 to work as a freelancer for Reuters TV, CNN, WTN and the BBC.
The Egyptian ambassador in London has been summoned to the Foreign Office to be informed of the UK's displeasure.
A Downing Street spokeswoman said: "The Prime Minister is completely appalled by the guilty verdicts delivered today.
"We are particularly concerned about the reports of procedural issues during the trial, including that key prosecution evidence was not made available to the defence team."