Now why would you want to

control the media?
You have been doing the wrong thing? Too bad. The world needs to know.
You are being criticised? Too bad. We all get criticised.
You want to hide something? Why?
You are about to break a promise you made? What, you have already broken it?
You want to get a message across? No other way to do it?
You want to silence the opposition? It's their job to oppose you.
The media is just being nasty to you? Really?
The media is stirring up a riot and you are in danger of losing control? Why are they stirring up a riot?
No doubt you can think of some more.
I had a look at a petition asking for more media control but I wonder if that is really what people want?  If I look at my little list then I think most people want the media to be free to inform people when someone of genuine public interest, such as an elected politician, has done the wrong thing. After all, we elect them. They are there to serve us. If they do the wrong thing then we need to know so that we will not re-elect them (if we are wise).  What we do not need to know is when their kid gets caught for speeding - and gets the heaviest possible penalty because of being "X's son or daughter" when another kid would get the minimum. It adds to the punishment of the child in order to embarrass the parent. That's wrong. 
In public life you have to expect criticism. It goes with the territory. The media has, on the whole, been very kind to our present government but why shouldn't they investigate wrongdoing? Why shouldn't the media inform the public about the misappropriation of union funds or company finances? Don't we need to know these things?
Break a promise? We elected you to do one thing, not the opposite thing. If there are good reasons not to do something we need to know - and that still does not excuse you for doing the opposite. If you want to do the opposite then go back and get yourselves elected on the opposite platform - if you can.
There are plenty of ways to get the message out there these days - as any savvy marketer can tell you. My youngest nephew can offer advice if you are still confused. His first degree is in economics and marketing.
Oh but really you do want to silence the opposition? That means they must be getting something right. No, they do not have to introduce their policies now. You would not introduce yours. You want them to put their policies up so you can "borrow" the bits you like and criticise the rest - thus deflecting discussion of your own.
The media is being nasty to you? Now that is not true, if anything they have been highly critical of the opposition in an effort to support you. You have had a dream run - and yes, I do understand you would like it to continue.
So the media is stirring up a riot is it? We have our own version of Tahrir Square? There has been a spate of car bombs? People are marching in their hundreds of thousands after church on Sundays? Hardly.
I don't think our media needs to be controlled by legislation. They need to obey other laws - like everyone else.  They need to be told there IS a difference between IN the public interest and OF public interest. The first is acceptable but the unwarranted intrusion into private lives which often forms the latter is not. That is all we need.
I suspect that, unpopular though that may be, it makes Leveson and our Finkelstein wrong and Cameron right - but the media will have to accept the difference between IN and OF and respect that difference.