Jeremy Moodey was speaking as David Cameron urged MPs to support airstrikes against the terrorist group in Syria.
The Prime Minister told MPs that IS' headquarters are in Syria, and that the only way to defeat them would be to strike them there.
He argued that bombing them would make Britain safer by making terrorist attacks less likely, and that it was the right thing to do given the recent massacres in Paris and Tunisia.
Several other countries are currently conducting airstrikes against IS targets in Syria. They include the US, France, Turkey, Saudi Arabia, Russia and Qatar. Britain is already conducting them in neighbouring Iraq.
Labour leader Jeremy Corbyn remains opposed to Syrian airstrikes, arguing that they will encourage further terrorist attacks against Britain as acts of revenge and kill innocent civilians.
Mr Corbyn advocates cutting off Islamic State funding sources, which include illegal oil selling and people from some Gulf states such as Saudi Arabia.
In the last Commons vote on the issue in 2013, a motion to bomb Islamic State was defeated by 285-272.
The Church of England approved military action in Syria to provide a safe route for refugees to leave the country, however they did not specify whether they supported airstrikes as part of this or not.
Jeremy Moodey, from Christian charity Embrace the Middle East, told Premier that in the Prime Minister's official documents outlining his position on the issue: "There's a statement right at the beginning [saying that] the terrorist attacks are 'planned and orchestrated in Syria'. There's no evidence for that. Much of the evidence has been that many of these terrorist attacks are orchestrated in Europe."
He also told Premier that David Cameron admitted himself that bombing alone is not enough to defeat Islamic State: "We've got the Kurds, but they're only interested in some parts of the territory. We've got some moderate opposition forces but they're weak and fractured. So who is going to do the hard work on the ground that is needed to back up the air attacks?
"There've been airstrikes against Isil in Syria for quite a while now, and there's no evidence that we're rolling them back. The main reason for that is because of the disorganisation and the lack of coordination between ground forces, and indeed competing objectives."
Listen to Premier's Aaron James speaking to Jeremy Moody here:
