In the UK, as stated for other countries, I would just use Pay As You Earn, where all taxes were extracted at the time of pay check, and would owe 0GBP at the end of the year. My Californian wife was astounded by this. "How do you know they've not got it wrong and screwed you?!" "Because I trust they got it right." "Why would you do that?!"
My read of the British is that they might not like the government or politicians, but they generally believe that government agencies get things to the letter of the law more often than not. You can disagree with the tax law, but you assume that the tax man is taking the right amount as governed by that law.
You can't pass tax reform in the US because enough of the citizenship wouldn't accept it.