Stephen Rasche, who represents the Chaldean archdiocese of Irbil, fears internally displaced Christians and other religious minorities will flee the country entirely.
On a brief visit to London, the external legal counsel member is due at Parliament on Thursday when he will call on the UK government to commit £5 million towards the "perilous" situation.
Speaking with Premier, Mr Rasche said: "The funding that we're looking for right now is emergency funding so that we can continue [helping] the medical, shelter, food and clothing needs.
"The concern is that, if we're not able to adequately provide these things, they will leave."
Mr Rasche fears the swift initial response by the private Christian community to assist believers in the region means they have subsequently missed out on UN means-tested aid.
He went on to say: "The entire welfare of the Christian community in northern Iraq has been paid for by private aid dollars - the entire thing up to this point."
Parts of northern Iraq are being liberated from Islamic State - on one side by the Iraqi army and various militias and Kurdish Peshmerga on the other; both sides are being assisted by American-led coalition forces.
Stephen Rasche, an associate of Aid to the Church in Need, said families displaced from the Nineveh Plains face having to wait at least another six months before they can return home - and aid is needed to support them until then.
He added: "These people still have another six-to-twelve months of a transition period before they can realistically begin to move back to Nineveh in a meaningful fashion because of all the destruction."
Listen to Premier's Alex Williams speaking with Stephen Rasche: