Ms Bibi spend eight years on death row after being convicted in 2010 of insulting the Prophet Muhammad during a row with neighbours. Her release from prison earlier this month, sparked widespread protests in the Islamic country with hardliners going “place to place” with photographs of her relatives who are living in fear. The 54-year-old mother-of-five is currently in protective custody, pending an appeal lodged by a religious party against her acquittal.
The widespread protests ended after the government agreed to preventing her leave Pakistan.
John Pontiflex, from Aid to the Church in Need UK, told the Guardian: “They have told me that mullahs had been reported in their neighbourhood going from house to house showing photos of family members on their phones, trying to hunt them down.
“The family have had to move from place to place to avoid detection. Sometimes they can only operate after sundown.
“They have had to cover their faces when they go out in public. They have had to remove the rosary that hangs from their car rear-view mirror for fear of attack.”
Her lawyer, Saiful Malook, has been granted temporary asylum in the Netherlands after facing death threats and Ms Bibi’s husband has pleaded for asylum.
Mr Malook told reporters: “I hope the western world is trying to help her.”
So far Canada, Spain and France are thought to have offered asylum.
The UK government has declined to answer questions about whether it is considering an offer of asylum, saying it does not want to further endanger Bibi and her family.
Mr Pontifex has called for more immediate action and protection for the family or they risk being killed.
He added: “If we continue to wring our hands over this case, there is a possibility that we will wake up one morning and find the family are dead.”
The case against Ms Bibi began after claims she had an argument with a group of women in June 2009.
At the time they were harvesting fruit when a row broke out about a bucket of water. The women said that because she had used a cup, they could no longer touch it, as her faith had made it unclean.
Prosecutors alleged that in the row which followed, the women said Ms Bibi should convert to Islam and that she made offensive comments about the Prophet Muhammad in response.
When acquitting her the Supreme Court said that the case was based on unreliable evidence and her confession was delivered in front of a crowd “threatening to kill her”.