It's after 26-year-old Shahzad Masih and his 24-year-old wife Shama Bibi who, was four months pregnant, were beaten, tortured and burned alive in a furnace.
They were attacked by a mob of Muslims after a claim they had ripped up a Koran was shouted from mosque loud speakers.
Director of Advocacy at the EA, Dr Dave Landrum, said this latest incident is a clear misuse of the country's blasphemy law to persecute Christians.
"This barbaric act represents the latest in a long line of brutal acts of religious intolerance against Christians in a country which is set to receive more than £400 million in aid from Christian taxpayers in the UK," he said.
He added that 'consideration should be given' to Pakistan's membership of the Commonwealth because of its failure to reform or repeal its blasphemy laws.
The Commonwealth is an association of 53 states that were previously members of the British Empire.
In 2013 it published a document, which all nations agreed to, stating: "We emphasise the need to promote tolerance, respect, understanding, moderation and religious freedom which are essential to the development of free and democratic societies, and recall that respect for the dignity of all human beings is critical to promoting peace and prosperity.
"We accept that diversity and understanding the richness of our multiple identities are fundamental to the Commonwealth's principles and approach."
In recent years blasphemy laws have been used by Muslims to settle personal vendettas against Christians and other minorities.
Meanwhile the head of the South Asian Forum of the Evangelical Alliance, Manoj Raithatha, has called on all Christians in the UK to sign a petition, by the British Pakistani Christian Association, calling on the UK government to put diplomatic pressure on Pakistan.
"We need 100,000 signatures on this petition which calls on the UK and other western governments to condemn and do something tangible to ensure that there can be no business as usual in Pakistan in relation to the murder of Christians under the pretence of its biased blasphemy law," he said.
He added: "It was shocking and horrifying that policemen stood by and watched the summary execution and did nothing to stop it.
"Pakistan needs to ensure that the impunity for hate attacks against minorities is stopped! And they can do this by guaranteeing that perpetrators are convicted rather than released after a short period of remand as in previous similar incidents."