This is not about suppressing a free media, it is about making it truly free. How can we say a press controlled by a few overseas media moguls (largely exempt from tax) is truly free? Do people think that a media reliant on advertising is free to criticise its advertisers? - mostly big business (this is one reason publicly funded media (like the BBC) is such an important part of the media mix.
Freedom is not about unbridled capitalism, as the 1930s demonstrated (yet the Right have managed to equate freedom with laissez faire in our minds). There is little freedom in a system that distorts so obviously. Inequality of power - like wealth and income inequality matters - and the media is inextricably linked with power - as Blair suggests - it is essential for a proper functioning democracy that the media is not only free but balanced. It is the media that helps hold governments to account on a daily basis between elections but to be truly free, it ironically needs some regulation. Just as business will ignore health and safety, environmental concerns and workers rights without government regulation - the media will ignore accuracy and quality of their output. We do need regulation - but it is nothing to do with suppressing the freedom of the press - on the contrary it will enhance it.