In an open letter published in the Independent newspaper, the group raised concerns about Mohammed Asghar’s wellbeing and asked the president of Pakistan to intervene.
Mr Asghar was arrested in 2010 in Rawalpindi, near Pakistan’s capital, Islamabad, for claiming to be the prophet Muhammad.
His family says he suffers from mental illness and was treated for paranoid schizophrenia in Edinburgh before returning to Pakistan in 2010.
He was convicted last month and his family immediately launched a campaign for him to be released from custody in order to receive medical help.
His lawyers said he appeared “pale, dehydrated, shaking and barely lucid” during a recent visit, prompting fears his condition has seriously deteriorated.
Signatories to the open letter include Labour’s shadow justice secretary Sadiq Khan, Scottish human rights lawyer Aamer Anwar, academics from the Muslim Institute, the Islamic Society of Britain and a host of charities.
The letter is addressed to Pakistan president Mamnoon Hussain.
It reads: “Like so many British Pakistanis, Mr Asghar was a successful businessman and pillar of the community who lived for many years in the UK where, through a lifetime of hard work, he helped promote the bonds of friendship and understanding between his native and adopted countries.
“We the undersigned are concerned that his recovery from illness is impossible whilst he remains detained at Adiala jail, where his lawyers fear he is in danger of taking his own life.
“We respectfully urge you to consider using your discretionary powers as president to pardon Mr Asghar and to allow him to be released from jail so that he can receive his treatment and be reunited with his loving family.”
The blasphemy complaint was brought against Mr Asghar by a tenant with whom he was having a dispute.
His family have appealed to the UK government to do everything it can to make sure he is safe.
In a statement released through the group Reprieve earlier this month, his relatives said: “As a result of a property dispute with one of his tenants, my father was jailed pending a trial.
“The dates kept being moved forward so that by the time the trial concluded, he had already been in horrific jail conditions, sharing a cell with several other men for three years.
“Throughout this time, he had minimum access to medication that might have helped his mental illness for three years.
“We are really upset and concerned that they will never release him and that he will die in jail.”
Meanwhile, a petition calling on both the First Minister Alex Salmond, and Prime Minister David Cameron to campaign for Mr Asghar’s life has attracted thousands of signatures.
The petition has been set up on campaigning website change.org by the chair of the Scottish Secular Society, Caroline Lynch.
Ms Lynch said earlier this month: “Secularists believe in freedom of speech and faith. We feel that no-one should suffer persecution for their beliefs, and blasphemy is an affront to human rights.
“David Cameron has expressed his concern, that the government is watching the situation carefully. Watching is not enough.”
The Scottish Government has confirmed that it remains in touch with the Foreign Office.