Cardinal Vincent Nichols told the BBC: "There is no way IS is going to walk away without being forced to do so".
The cardinal has just returned from Iraq's Kurdish capital Erbil, where he visited some of the Christians who have fled from the threat of IS.
He said: "IS threat has got to be pushed back territorially."
Last August, 125,000 Christian refugees from Iraq's Nineveh Plains flooded into Erbil in one night alone.
The influx of refugees from 13 Christian towns and villages has "changed the face" of Erbil, the cardinal said.
With the population of the region ballooning by 30%, a financial crisis has been brewing for several months following a budget dispute with Baghdad.
BBC Middle East editor Jeremy Bowen says the delicate mosaic of different faiths in the area has been shattered since the US-led invasion of 2003.
The population of Iraqi Christians has fallen by half and a very diverse, deeply rooted Christian tradition has suffered grievous blows, our correspondent says.
Speaking to BBC Radio 4's Today programme, Cardinal Nichols said he went to Erbil to "express solidarity" with the people who have been traumatised.
Returning home "full of admiration" for the local churches, he said the tens of thousands of people sleeping in parks last year had now all received "solid accommodation" in caravans or houses but this was just the first step.
"They want their villages back - the IS threat has got to be pushed back territorially," the cardinal said.
Yet even if IS do leave, the cardinal pointed out that "specialist help" would be needed to make the villages safe to live in.
He said: "We know IS - they are just destroyers - they would leave villages not only wrecked but booby trapped".
The fabric of the society "really depends on the presence of Christians", the cardinal added.
The head of the Roman Catholic Church in England and Wales has said removing Islamic State (IS) by force "has to be achieved" for peace in Iraq.