Jasmine Rana travelled to present the 70,000-signature petition demanding action in the case of 70-year-old Mohammad Asghar who was convicted of blasphemy.
Ms Rana, 40, thanked everyone who is backing the demand to have her father returned to the UK after he was shot and injured in Adiala prison in Rawalpindi last month.
She said: “Since then we have been working with the Scottish and the British governments to urge the Punjab authorities to acknowledge my dad’s mental illness and to ensure his safety, but they have not taken our requests seriously.
“They are even refusing to give us access to information about my dad’s mental health and about what really happened in Adiala prison on the day he was shot.
“My dad has spent a very long four years in prison without proper treatment for his illness. His life remains at risk for as long as he is held in Pakistan. I have come to London today to ask the Prime Minister to intervene to bring Dad back home. It must end now - he has suffered enough.”
Mr Asghar was sentenced to death in January after he was found guilty of writing letters to a number of people claiming he was a prophet.
The grandfather, said to suffer from paranoid schizophrenia, was arrested in 2010 following a complaint by a tenant with whom he was having a dispute.
Insulting the Koran or the Prophet Mohammed can be punished with life imprisonment or death in Pakistan, and those accused of blasphemy are at high risk of attack.
Mr Asghar has filed an appeal against his sentence but it may take several years to reach court.
His daughter and family solicitor Aamer Anwar had hoped to meet Mr Cameron today but instead held talks with with Foreign Office minister Tobias Ellwood.
Mr Anwar said the meeting had been “positive and robust”.
He said: “David Cameron must understand that words are no longer enough. Every second that Mohammad Asghar remains in Pakistan increases the likelihood of his death.
“Jasmine said today that her family has had enough of Pakistan’s broken promises and is disappointed that Mr Cameron failed to meet with her.
“Yet her family cannot thank enough the thousands of people who have offered their solidarity and prayers for her father. The Prime Minister must now personally intervene with the Pakistani government. They must understand that after four long years it is time to send home a seriously ill old man before it is too late.”
Scotland’s First Minister Alex Salmond has said he is “extremely concerned” about Mr Asghar’s welfare and would support a prisoner transfer agreement.
A Downing Street spokeswoman said this week that the Government has repeatedly raised Mr Asghar’s case “at senior levels” and is working to ensure that he is receiving the best possible support.