The Independent might as well be the official state outlet of the EU as far as I can tell. You'd get more balanced coverage from reading Chinese media about China. Just taking a few representative headlines from its website:
I actually agree, I (maybe consciously, maybe subconsciously) choose to read the news from the left, since the United Kingdom doesn't really have balanced news. The BBC, for example, might as well be the official state outlet of the Conservatives and American news democrats, with their outright disdain for Corbyn, and their refusal (with late acceptance) to publish stories about DNC leaks – I'm forced to pay for the BBC, I'm not forced to pay for news from the left.
If you deliberately seek out news sources you know to be biased, and then compare them to other news sources, aren't you always going to conclude that those other sources are biased in the other direction?
You say the BBC has "outright disdain" for Corbyn but in my experience BBC News does manage to do a pretty good job of being unbiased. Are you sure that they aren't just reporting an unfiltered flow of stories and many of them happy to be pretty negative, thus they may seem to be biased?
http://www.independent.co.uk/topic/brexit
"Why there could be post-Brexit riots this summer"
"Ford to consider closing UK factories in Leave towns after Brexit"
"The only way to save Britain after Brexit? Stop London's dominance"
"Brexit blamed for Bank of Japan monetary stimulus plans"
"Brexit doesn't make me proud to be British"
"I've been mapping kindness across the country to tackle racism"
"Why our post-Brexit economy can't be saved by slashing interest rates"
"Revealed: the shocking scale of racist hate since the Brexit vote"
"Incident by incident – the grim litany of post-Brexit hate crime"