How influential is the Press?

http://www.guardian.co.uk/media/greenslade/2011/jun/21/national-newspapers-newspapers
This is an interesting question in the light of the ever-decreasing circulations of papers in the UK.
Though for many years papers like The Sun have loved to claim that their backing of one party or another has been pivotal in it winning the General Election, the reality, as this study shows, has not been a true positive correlation.
But despite that they’ve managed to retain their influence over the national leaders by acting as if it is true (and which leader would risk going against them in case it was?).
Whatever the truth of how much they can tip voters one way or another there are two undeniable things here — the news agenda is still set a lot of the time by stories in the Press and that the constant drip of coverage for or against parties and their leaders must have an impression, unconscious or not, on the perception of parties and leaders and that it’s that which party leaders fear most.
And when that’s going on to as many readers as the Press have daily (still an impressive number) then it’s fair to argue that while the Press in print is on its way down, its influence is still huge.
Unless and until new media separate from the Press titles establish an equivalent level or credibility and readership, the Press will remain influential, if not masters of what we think.