The Independent is very pro Remain as is the 'i' . On a local basis the three main newspapers in Scotland are now Remain The Herald, Scotsman and The Record.I was really thinking about social media coverage, but I suppose that this is often driven by the print media.
I certainly agree with your second paragraph - newspapers are very keen to please their advertisers. There is some suggestion that the Daily Mail's 'stutter' in its pro-Brexit coverage when Geordie Greig took over as editor was because the paper was concerned at how the advertisers felt about leaving the EU.
I can't agree with you that the (print) media is all pro remain - in fact if it were, then there would not have been any space in the market for the pro-remain weekly 'The New European'. The Guardian is the only unambiguously remain leaning general newspaper. I say 'general' because I suppose you could also put the FT in that category.
Given that position, surely the leave leading papers should be promoting the benefits of leaving rather than simply rubbishing the EU. After all being in the EU is the status quo, surely the onus on people promoting leaving is to demonstrate how things are going to be at least as good, if not better after the UK leaves?
I just think it is interesting that I see a lot of negative stuff about the EU but very little about what the benefits of Brexit are going to be.
The Evening Standard which although a London paper is an influential paper is Remain.
It is a lot easier to look for Remain backing media sources (much longer list) than it is to find Brexit backing ones(very short list).
I suspect there will be a change in tone once Brexit happens.