Pastor Zafar Bhatti, 56, was sentenced to life imprisonment for blasphemy, a charge he denies.
His most recent appeal hearing was reportedly postponed because the presiding judge was due to go on holiday.
A statement from the British Pakistani Christian Association (BPCA) said in a statement sent to Premier: "The case was moving favourably in the direction of Zafar but Justice Raja Shahid Mahmood Abbasi sought a postponement as he would not have time to complete paperwork before existing travel plans.
"Despite the fervent remonstrations by Advocate Tahir Bashir for a decision to be made to release Pastor Zafar the judge said such a decision could not be made as he was off on holiday and had booked flights."
The court has set 12th September 2019 for the new appeal date for Pastor Zafar.
The pastor founded and led a small NGO called Jesus World Mission to assist the poor.
A local Islamic leader filed a complaint at a police station in Rawalpindi and claimed the pastor had been sent messages from an unregistered number insulting the Muslim Prophet Mohammed and his mother.
Pastor Bhatti has experienced pressure from Muslim prisoners to convert to Islam and has been beaten several times, the charity has reported.
There are also growing concerns for his health since he has developed diabetes since being imprisoned and experiences heart pain and headaches.
Juliet Chowdhry, Trustee for the (BPCA), said: "An innocent disabled man has been rotting in a Pakistani prison for coming up to seven years and yet few people bat an eyelid.
"The mysterious text cannot even be linked to the prisoner and no evidence exists that Zafar was even remotely involved in the crime, which for all intents and purposes seems very contrived.
"It beggars belief that a judge can cause a delay of three months to the release of an innocent man who is near his wits end, simply because he is going on a holiday.
"Serious reforms of the Pakistani Judicial system are required so that administrative tasks can be shared with others to see justice done expediently."
Penalties for blasphemy in Pakistan range from a fine to death.
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