I wouldn't agree with the notion that this is a small minority at all:
There are few surveys that have produced very similar results:
In a 2007 Pew Research poll in response to a question on whether suicide bombing and other forms of violence against civilian targets to defend Islam could be justified,[27] in Europe:
64% of Muslims in France believed it could never be justified, 19% believed it could be justified rarely, 10% sometimes, and 6% thought it could be justified often.
70% of Muslims in Britain believed it could never be justified, 9% believed it could be justified rarely, 12% sometimes, and 3% thought it could be justified often.
83% of Muslims in Germany believed it could never be justified, 6% believed it could be justified rarely, 6% sometimes, and 1% thought it could be justified often.
69% of Muslims in Spain believed it could never be justified, 9% believed it could be justified rarely, 10 % sometimes, and 6% thought it could be justified often.
This is just in relation to acts of terrorism against civilians. 35% of Muslims in france think it can be justified in some circumstances, 24% in Britain. A minority yes but not a small one.
And this is just in relation to terrorism. When the questions are around opposition to western values the numbers are closer to 50%.
We are in the middle of a hearts and minds battle with moderate muslims and it's on a knife edge.