Speaking to Premier from Islamabad, Mehwish Bhatti from the British Pakistani Christian Association said: "There are so many blasphemy victims - Christian victims - who are still in prison and are on death sentence like Asia Bibi".
She was accused of making insulting remarks about Islam after her Muslim neighbours objected to her drinking water from their glass because she was Christian. They asked her to convert to Islam, which Asia refused.
Bibi has always denied blaspheming.
Earlier, the far-right TLP threatened to hold countrywide demonstrations if Bibi was acquitted.
Ms. Bibi's case also has been high on the agenda of religious hardliners in Pakistan, many of whom are fiercely opposed to her release.
Taseer later gunned down in broad daylight in Islamabad in 2011 by one of his own bodyguards who cited the governor's position on reforming the country's blasphemy laws as the motive.
Her appeal case is now pending with the Supreme Court of Pakistan. But in Pakistan, it has rallied radical Islamists and militant groups who have embraced Pakistan's controversial blasphemy law, using it to cultivate support and attack those who try to break their power. At least 1,472 people were charged under Pakistan's blasphemy laws between 1987 and 2016, according to statistics collected by the Center for Social Justice, a Lahore-based group.
Human Rights organisations went to Supreme Court of Pakistan and Supreme Court suspended Bibi's death sentence for the duration of the appeals process.
On Wednesday, the judges noted that no solid evidence of wrongdoing by Bibi was presented before the court.
Her daughter, Eisham Ashiq, had previously told the AFP news agency that if she were released: "I will hug her and will cry meeting her and will thank God that he has got her released". "Pakistan's Supreme Court must be appreciated that it upheld the law of the land and didn't succumb to any pressure".
Rt Rev Susan Brown said: 'We urge the authorities in Pakistan to do all in their power to ensure the safety and security of Asia Bibi and her family, her lawyers and the judges. The argument escalated as insults were traded with the women later accusing Bibi of committing blasphemy during the exchange. The women said that because she had used a cup, they could no longer touch it, as her faith had made it unclean. Dozens have been killed following blasphemy claims, sometimes by mobs of men.
"Finally Asia Bibi has won", her lawyer, Saiful Malook, told The Times.
The group's emir for the Khyber Pakhtunkhwa province said: "The objective of this protest is to raise awareness that if any such judgment is delivered in this sensitive case that grants concessions to the blasphemer Asia, then we will protest all over the country".
"We are grateful to the judges for giving us justice".