This is difficult to answer, as the media in the UK has taken an obvious down-turn in the past 3 or so years. I'm not sure if there is even a UK equivalent of a WaPo for the UK - something that's balanced, but centre/centre-left (sorry, I don't think much of the NYT, and canceled my subscription with them a few months ago
).
The Times is Murdoch owned, and so has a right-wing bias.
The Independent is trashy verging on clickbait rubbish since they turned digital-only a year or two ago.
The Guardian has lost its way since Rusbridger left/was pushed out a few years back. Though it's probably the best for politics, avoid/ignore everything that's an Opinion/Op-Ed piece, and prepare to read very critically. It's not what it once was - and is unexpectdly right-wing at times - but will do the job. The Observer is the Sundays-only partner of The Guardian, btw.
The Telegraph is right-wing, but without the Murdoch influence. Used to have one of the best Business sections in UK media, not sure if it still does.
It's the only paper that might be worth considering instead of The Guardian.
Burn in a fire: Daily Express, Daily Mail, The Sun, The Star.
Edit: My personal reading habits are glance at the front page of The Independent and Telegraph, and read the foreign news section of The Washington Post.