The unrest was sparked over an omitted reference to Islam's Prophet Mohammed in a parliamentary bill.
Leighton Medley from the British Pakistani Christian Association told Premier he was forced to flee with his wife on Sunday while on a missionary trip in the country.
He said: "There were many ...trucks that were parked up there ...and I was the only Westerner and I started to get quite a few funny looks - being the only Western presence there.
"There have been reports of kidnapping in the past so I had to relocate."
At least two people died and more than 250 others were injured in street demonstrations as protesters clashed with security forces.
The Islamists for the past three weeks have been demanding for the country's law minister to resign for the change in the electoral oath that omitted declaring prophet Muhammed the last of the prophets.
Zahid Hamid apologised for the omission in the bill, saying it was a clerical error that was later corrected, but the Islamists persisted, taking to the streets and setting up a sit-in at the Faizabad intersection on the edge of the Pakistani capital.
On Monday, a sense of peace was restored as protesters took to the streets to celebrate Mr Hamid's resignation.
The Tehreek-i-Labaik Ya Rasool Allah party, which was behind a sit-in in Islamabad and protests in other cities and towns across Pakistan, said they were dispersing peacefully under an agreement with the government.
Under the new deal, the Islamists also agreed not to issue a fatwa, which is a Muslim edict that could endanger Mr Hamid.
Wilson Chowdhry, Chairman of the British Pakistani Christian Association had questioned whether to continue with the rest or the charity's outreach programme in Pakistan.
He said in a statement: "We are extremely concerned about the safety of our missionaries Brother Leighton and his wife Pana whilst they are in Pakistan.
"If the level of rioting across Pakistan increases or remains the same we will have no option but to terminate our current mission programme."
Security forces have started removing shipping containers surrounding the sit-in that had been placed in a bid to prevent the protest from spreading deeper into the city.
Medley told Premier that despite fearing for his safety, he was already planning another trip back to Pakistan once he leaves back to the UK.
He added: "We need to work together and as Christians, we need to have faith in God, we need to pray to God and we need to walk in grace.
"We need to pray for those who don't necessarily share our world view."