Well, the Sun seems to believe they were critical to the Brexit vote and they are the largest circulation newspaper in the UK:
https://www.thesun.co.uk/news/1338543/our-paper-led-the-figh...
The Economist, Financial Times, The Guardian, New Statesman, The Observer, The Independent, The Scotsman, The Times, Daily Mirror, London Evening Standard, British Medical Journal, Daily Mirror, Daily Record, The National, Sunday Mail, Sunday Mirror.
Someone would have to have an extremely convincing argument to persuade the majority that the media were not almost totally for Remain (including the BBC).
Lets say for argument it was 50/50. I could definitely understand why people might have the (in this example, incorrect) perception that the majority of newspapers were for remain. As papers are seen as part of the establishment, and the non-newspaper establishment was so heavily remain, it could easily bias your perception of coverage.
"So facts don't matter only what the presented image of what the "majority" thinks?"
Facts do matter, I just believe that the majority have this view of Brexit news coverage for a variety of understandable reasons.
Papers like the Daily Telegraph and the Daily Mail pretty much epitomize the UK "establishment" and they've been hostile to the EU/EEC for decades.
As is covered in great depth, touching on some interesting HN relevant topics like complexity theory, this was a huge campaign with many moving parts, motivations, draws and repellents.
Telling yourself it is simple as "those who don't hold my opinion were only persuaded by lies as they are stupid" is a virus that holds you back from understanding and amplifies and reinforces your prejudices.
Massive amount of very interesting info in this article that covers a wide range of strategy and persuasion topics.
edit: re-reading your post made me realise you have almost definitely have not read the article if you believe the press were on their side