I feel I should step in at this point with a note about Sharia law. Sharia is, as everyone knows, Islamic law. That does not mean all forms and interpretations of Sharia are the same, it's become very much a hate word for many anti-fundamentalists in the west as a result of extreme practices that are part of it in some aggressive readings and interpretations. I'm not denying that I really, really don't want extensions of Islamic law further into the public sphere, as for me law is and should be fundamentally a civil, secular form of jurisdiction. Nevertheless, throwing the term Sharia around like evil confetti isn't particularly accurate, as pretty much all Muslims would claim to be following sharia; the difference between extremists and radically liberal groups like Imaan (the UK's Muslim LGBT movement) is essentially based upon interpretation.
So, my thoughts, in no real order.
-> Yes, fundamentalist Islam is still a big problem, that should have been obvious really.
-> "Letting people stay" is not the issue as a large number of radicalised people are British. That disgusting video, with the guy with blood on his hands. He has a London accent. These people are often not first generation immigrants and quite a lot aren't even from Islamic family backgrounds (it's a general rule of religion that new converts tend to have twice the zeal of those who've just been passive brought up with a religion). We can't just kick them out, they have nowhere to be kicked to; they're our problem.
-> So what do we need to do? Firstly, target leadership structures and preaching, secondly, start putting out positive counter-messages. The worldwide fight against religious extremism may be partly fought with guns, but it can only be won with books (or, more likely, YouTube videos). A lot of Islamic terrorists are not evil genii; they're young lads who get a bunch of armadilloe poured into their head about all the things suffered by the Islamic world and how noble it is to fight etc etc - a lot of them are really probably a bit dim, and it's this "human resources" pool for terrorism that we need to make dry up. We can do that firstly by counter-arguing more effectively (because a lot of what these people are being fed is straight up lies), and secondly by discrediting the nutters who spout it to begin with.
-> What do we not need to do? Hold a fracking COBRA meeting and act as panicked as possible. This is political points-scoring and Cameron trying to look Prime Ministerial and in control. If we panic the whole country and hold top level emergency security meetings for a single murder, how effective are we claiming terrorism is and how much are we encouraging copycat attacks? There is absolutely nothing Cameron can do to make this situation better. Yes, it's a serious incident, yes, it deserves a serious and measured response, preferably a private visit to the family involved. This panic strategy is just a piece of showmanship by a scared Prime Minister with a fragile grip on his party.