Leveson's report presents a big problem for Cameron

Prime Minister David Cameron Photo: Danny Lawson/PA Wire

There were a few surprises, but Lord Justice Leveson's report ended up roughly where most predicted it would.

He flayed the press, gave the politicians a mild rap on the knuckles, cleared the police and suggested a new regulator whose independence would be overseen by Ofcom - the body that currently regulates broadcasters.

There were a few clever twists: The system offering arbitration to lower libel costs might well appeal to newspapers. And the fact that the supervisory body is at one remove would allow supporters of the move to claim more or less accurately that the press will still be able to regulate itself.

But the big question is, what happens next? What becomes of it?

Lord Justice Leveson with his report Credit: Gareth Fuller/PA Wire

The newspapers have always been confident that they have the Prime Minister where they want on this issue, but I think that confidence may have been misplaced.

It is true that the early mood music out of Downing Street suggests that the Prime Minister will outline several key reservations when he gets to his feet in the House of Commons this afternoon.

But he has a pretty big problem, which is that there is every chance he doesn't command a parliamentary majority on the subject.

It is not clear what Deputy Prime Minister Nick Clegg will say in his separate statement on the Leveson report Credit: PA Wire/PA Wire

Nick Clegg's aides are still being a little cagey as to exactly what he will say in the House, but they do confirm he will be making a separate statement (in itself a remarkable event). It seems clear that he is going to back an independent regulator overseen by Ofcom or a similar body.

So, there is a split. And given that Nick Clegg and Ed Miliband both say privately they believe this issue is of critical importance, there is every chance that they will choose to ambush the Prime Minister at some point on it.

If and when this happens - and if he loses - David Cameron risks looking like a Prime Minister who is in office but not in power. And this relates to an issue upon which the public may well be more inclined to agree with his opponents.

If this concerned any other subject, the press would argue this situation would result in a politically fatal loss of authority.