That the British press is generally pro-Brexit is true. But as so often The Guardian manages to take the wrong lesson from this observation:
In 1975, the last time the UK went to the polls over the issue of EU membership, the yes vote won by a very comfortable margin – 67.2% to 32.8%. On that occasion, however, the entire national press was vociferously in support of staying in. The Daily Express, Daily Mail, Daily Telegraph, Times, Guardian, Sun, Mirror and Financial Times all spoke with one voice: it must be “yes”.
Those committed to keeping Britain in the EU can only dream of such a day this time. While most of the papers are yet to formally declare their position, Europhiles can confidently count on a much smaller number of supportive front pages on newsstands on 23 June.
The mistake is to think that newspapers (or other media outlets) lead or form public opinion. That's not what they do at all: they follow it. It is not true that the highly paid staff of the Daily Mail believe that everything either causes or cures cancer, nor that everything including cancer affects house prices. It's that they believe that's what their readership think and or are interested in.
So it is with more political things such as British membership or not of the European Union. Newspaper editors simply are not pondering the subject and then thinking about what they should persuade their readership of. Instead, they're trying very hard to work out what it is that their readership already believes and then pander to those beliefs. As the above notes, they got it largely right in 1975. The majority of the country was pro-EU and so was the majority of Fleet Street. Similarly The Sun does not consider the relevant manifestos before plumping for Labour or Tory. Instead, it tries to work out what the readership of that paper is likely to vote for.
So it is now: the papers can see that there's rather more opposition to the EU than there used to be and are thus trying to get out in front of their own market.
Please do note that we are not calling this one way or the other: nor, despite the well known views of some of us are here here advising either way. This is simply an observation about how the media works. They attempt, as best they can, to reflect the beliefs they think their market already holds. Thus some majority of them being pro-Brexit means, and this is all it means, that those running those newspapers think that some substantial portion of the population is pro-Brexit.