It is of course true that Cameron should have studied Islam independently from the Conservative Muslim Forum, Baroness Sayeeda Warsi (the unelected Minister for Faith and Communities) and his advisers (i.e., the higher civil servants). After all, he was 35 years when 9/11 occurred and 39 when 7/7 occurred in the city of London. He will now also know about the massive Muslim grooming of young non-Muslim girls in the UK. He knows about the 85 or more sharia courts in his country, the weekly political activism of Islamists on the streets of the UK, the 15 foiled Islamic terrorist attacks between only 2005 and 2008, etc. He also knows about the the Taliban, the Islamic civil wars in Iraq and Syria. He may even know about the Islamist slaughter of over one and a half million Sudanese Christians and black animists in the 1990s and 2000s.
In fact David Cameron is even on record as having criticised what he then called “Islamists”. That was in 2005. The “neoconservative” writer, Douglas Murray, at around about the same time, also suggested that things should be done to slow down the Islamisation .... What happened then? The Conservative Party ostracised him. In addition, a Conservative Party MP by the name of Michael Gove wrote a book, in 2006, called Celsius 7/7. This book is about Islamism and the threat of Islamic terrorism in Europe. Michael Gove has been almost silent on these issues ever since. You may have heard of him: he's now the Sectary of State for Education; working under no other than David Cameron.
More relevantly, Cameron might have even read the Koran. However, what's likely to have happened is that he has been fed various nice and innocuous extracts from that book advisers and Tory Muslims (as well as by non-Tory Muslim individuals and Islamic groups). However, I doubt that he voluntarily picked it and read it before 2010. In mention this because Tony Blair, infamously, once claimed that he reads the Koran every night. Despite that, as a public relations man, and someone who, to me, comes across as quite politically and philosophically shallow, I doubt that David Cameron had read any part of the Koran before he became Prime Minister.
Since David Cameron became Prime Minister, he might have spent a few hours maximum independently and truly studying Islam. But he most certainly won't have chosen his own works to study. What will have happened, again, is that his civil servants, or perhaps certain Islamophile Tory MPs, or Muslims within the party, will have supplied him with some Islam-friendly literature. He would have read all that and taken most of it at face value quite simply because he literally hasn't got the time to study Islam in detail, let alone be critical. Besides which, Cameron will acquire the information he needs in order to be a successful politician. And being a critic of Islam, he may well think, will never pay him political dividends.
If the "Islam issue" were as pressing for him as debates about tax, the NHS, competition with the Labour Party, sustaining his own rule within the Tory Party, etc.; then he would indeed have studied it in detail. However, although the Islam issue is pressing for the UK and indeed the world as a whole, it's not pressing issue for David Cameron himself. Not in the least. In fact, from what he's said recently, and indeed from what he's done (e.g., making London the “Islamic finance capital of the world”), I would say that ingratiating himself with Islam and the Muslim community-of-votes (large parts of which tend to vote in blocks) has been (fairly) pressing for him.
David Cameron will almost certainly be out of power within the next ten years - probably much sooner. Thus why on earth would it be important to him, as a shallow power-only politician, to do a critical study of Islam? It is utterly irrelevant to him. The only time Islam becomes relevant to Cameron is when it impinges on his own power and his own party's political influence: as with sharia finance in London and when he needs to prove his commitment to Community Cohesion and Diversity (at least to his Liberal and Leftist detractors). To expect anything else from Cameron is naive.
When I say that Cameron relies on his advisers and Tory Muslims to tell him what passes for the truth about Islam, I'm not passing the buck. Cameron is still culpable. The point is that this is how it will work in practice for such a busy man. That is, he will get almost all his advice on Islam from third parties. He is of course politically responsible for such self-willed ignorance. And it is also very likely that he knows he's ignorant on Islam. Despite that, he may not care that much. As I said, he won't be in power when the shit hits the fan (although in many cases it has already hit the fan -even in the UK). In fact there's even a possibility that David Cameron knows the full destructive reality of Islam but he still doesn't care that much; at least not politically-speaking or career-wise.
If Cameron were anything like Winston Churchill, he would think for himself about Islam. But he's not at all like Winston Churchill. Given the type of man he is, and the political situation we are in at the moment, it is naive to expect anything else from this particular politician. We could expect something else from a better politician; but not from him. After all, this man was weened in the public relations industry. He is very shallow, politically; though he's not so shallow when it comes to his own self-aggrandisement.
Quite simply, it would be impossible for the Tory Party to be critical of Islam itself because of the inevitable massive backlash from Britain’s three to five million Muslims; as well as from the Islamophile battalions of the Left. And even though 75% of Brits believe that Islam is incompatible with Western civili..., and 40% of Brits think civil war is inevitable and 59% think it is likely, that backlash against speaking such truths (or opinions) would still be too much for a present-day political party to cope with. In ten years' time things may be better politically (though not demographically). But, then again, they could also be much worse.
In point of fact I don't even think UKIP would ever get away with being critical of Islam in any way; at least not at the present moment in time. Indeed this party is already watering down its positions on immigration and suchlike. Who knows, in five years' time UKIP may have fully embraced the EU.
Basically, there is nowhere for David Cameron, the British Prime Minister, to move on this issue. Or, more correctly, there is nowhere he will be allowed to move. He is obliged to say what he says and do what he does.