Well Russia and the US seem to be getting on a bit better these days so maybe Putin would rather come onto the Anglo Saxon side.
But in all seriousness, that does not seem to be the way things are developing at all, not to me anyway. Britain's appetite for invading / liberating countries is pretty low right now, we voted against taking action in Syria. Trump talks about how NATO is no longer useful and the US should stop interfering in other countries. Im not saying these are positive things of course, he could extend that to refusing protecting European countries from a Russian invasion.
And while yes Islamists have every reason to hate the UK and US more than the EU, it seems like France and Belgium are easy pickings for them. So yes, of course you are right the UK needs EU help with security, but its not like Britain taking its warmongering ways and leaving is going to make the EU some kind of Utopia where terrorists no longer have any ambitions.