Thousands have had to flee the country, many in the city of Mosul who have been given an ultimatum by the extremist group ISIS to convert to Islam, pay a tax or face death.
One Iraqi bishop told Premier it's left just a 'handful' of Christian families there.
The Bishop of Manchester, Rt Revd David Walker, spoke on Premier's 'News Hour', he said:"I think what we need is a clear statement from the Prime Minister, so the UK borders agency are in no doubt whatsoever that if applications come in from those Christians being displaced by ISIS in Northern Iraq that they will be dealt with in a very favourable manner".
Last month, France said it would welcome those seeking refuge from Iraq.
In a joint statement, the Foreign and Interior Ministers said: "We are providing aid to displaced people fleeing from the threats of Islamic State and who have sought refuge in Kurdistan.
"We are ready, if they wish, to facilitate their asylum on our soil".
But the decision wasn't met with support from the Archbishop of Lyon who said it could 'exacerbate the exodus' from the country.
Cardinal Philippe Barbarin of Lyon said it's a generous act but could mean Iraq is left with no Christians at all.
Bishop of Manchester, Rt Revd David Walker: