What a bizarre line of argument. Are you saying the influence of the right wing press can simply be discounted because there are also other influences on the way people vote? Further, your belief that The Sun - for instance - merely reflects rather than influences public opinion is, to put it mildly, highly questionable.
I find your line of argument rather wearisome too. There's been quite a bit of research which indicates that the Sun's influence is not decisive and it could well be a case of newspapers echoing the views of their readers rather than forming them. In some studies voting patterns of readers of particular newspapers have followed the trends of those who read no newspapers at all.
www.sciencedirect.com/science/article/pii/S0049089X15001854
blogs.channel4.com/factcheck/factcheck-sun-win-elections/20827
www.city.ac.uk/news/2015/april/newspapers-influence-election
www.independent.co.uk/news/it-wasnt-the-sun-wot-won-it-official-1364910.html
It's too nebulous a subject for any truly decisive verdict, but the idea that the right wing press decide the outcome of elections is demonstratably untrue and is merely a convenient left wing trope to absolve themselves of responsibility when they seem to be incapable of making themselves electable.
You're also missing the impact of self selection. Nobody is forced to consume these papers, and in general they will normally choose a newspaper which reflects attitudes they already hold, rather than simply being ciphers with no opinions who are filled like empty vessels based on a random choice of newspaper.