Do you live in the UK? It's hard for non-residents to understand the impact of The Sun. It's the most read newspaper by far - having a greater readership than all the other papers you mentioned combined.
After the victory of John Major in 1992, the Sun ran the headline 'IT'S THE SUN WOT WON IT', a line that's since become a sort of mantra in english politics - nobody has won an election since without the support of The Sun.
The second most read is the Daily Mail, another euroskeptic paper. In fact, if you look down the list of papers by readership [1], you can see the euroskeptic press (Telegraph, Mail, Murdoch papers) is almost the entirety of newspapers that are in circulation.
I'm not saying there's some vast conspiracy. I'm just saying that Rupert Murdoch is not a fan of large, big-state regulatory projects, and as a result, his papers (which include the Times, for instance) have followed an anti-EU line. He traditionally takes a very active role in this kind of editorial decision making, and is very public about this fact.
Obviously, the establishment in england are traditionally liberal, internationalist, and the argument for Brexit is a hard sell on pragmatic grounds for obvious reasons - and that's why the vast majority of powerful people were against Brexit, and it took 'outsiders' to push the campaign through.
However, these 'outsiders' were able to do so because they knew the issue sold well with both conservative core demographics and swing voters. And, if you think that your average midlands swing voter would have opinions about supra-national trade standards without some serious narrative building, I have a bridge to sell you.
[1] - https://www.statista.com/statistics/529060/uk-newspaper-mark...