The BBC specifically has a trust issue in the UK. Even one of its own long term journalists wrote a book called "Can we trust the BBC?" (spoiler warning: the given answer is no).
Tax-funded institutions that are not accountable to the people paying the tax is corrosive. Resentment builds and has nowhere to go. For now at least if you're willing to disconnect from broadcast television entirely, you can avoid paying the license fee. But similar license fees in other countries have been adapted to include the internet; it's hard to know if the same will happen in the UK.
My favourite recent example of ridiculous tabloid-level BBC journalism is "Brexit threat to sandwiches":
Staying in the EU for a bit longer would keep the chiller cabinet full of sandwiches - but it would doubtless raise the political temperature.
The story literally argues that the UK would not have sandwiches anymore if no deal with the EU is reached. The sandwich was invented in the UK.
This is hardly an isolated example. Consider what sort of journalistic process led to this story being written, edited, reviewed and approved for publication. Is it one citizens should be forced to fund? What does that sort of thing do long term? Is it any wonder that trust in the press is in long term decline in the UK?