Nawaz Sharif stepped down after the country's Supreme Court decided to disqualify him.
Despite having reservations about the court's order, Mr Sharif decided to "show his respect for the judiciary and rule of law".
Wilson Chowdhry, Chairman of the British Pakistani Christian Association, told Premier his concerns following the Mr Sharif's decision.
During Premier's News Hour, Chowdhry explained: "Nawaz Sharif, with his party - the Pakistan Muslim League-Nawaz (PML-N), have actually bought in many laws and many changes to the life of the minorities living there.
"I'm worried about the advance of that and whether now we're going to see a return back to the heavy persecution that Christians and other minorities suffered previously.
"The persecution is ongoing but there does seem to be stronger laws in place and there does seem to be a better means for getting justice for minorities under his government than in previous governments. But it is still essential that we remove corruption from the political sphere in Pakistan."
A probe into Mr Sharif's family's wealth began in 2016 after documents leaked from a Panama-based law firm indicated his children had offshore companies.
It is not immediately clear who will succeed Mr Sharif, however his brother Shehbaz, who is chief minister of Punjab province, is seen as a strong contender for the job.
Pakistan's ruling party, PML-N, will be permitted by the speaker of the National Assembly to select an interim prime minister to rule until the 2018 general election.
Listen to Wilson Chowdhry speaking with Premier's Eno Adeogun:
