I was listening to the Beatles at a very young age (like, 5 - my dad played them all the time) and I remember he used to have me pick out which of them was singing. I used to think that Paul McCartney was American. “Paul is British?” I asked my dad in surprise when he explained the band’s history to me. I had been exposed to Monty Python back then and I had a good idea of what a British person sounded like compared to an American. I thought Paul sounded totally American.
To be fair, the Python lot don’t exactly sound the same as a typical scouser!
Sorry, but I just don’t hear it. The guy sounds like he’s straight out of Kansas, not England.
Overall, my point is, if you had no idea where Coldplay was from, the average listener wouldn’t be able to tell they were English. Test it out. Find someone who doesn’t know about Coldplay (like an older person) and play a few songs for them, then ask them where they sound like they’re from. I just did it to my mom and she said with a questionable glare, “Seattle?” 
When the Beatles first landed in New York in 1964, they had a press conference.
Reporter: Why do you sing like Americans but speak with an English accent?
Lennon: It sells better.
Even in “Yellow”?
Another one – you know that 80s hit “Come on Eileen” by Dexy’s Midnight Runners? Listen to the opening verse “Poor old Johnny Ray”. Does that sound like it could have come from a Kansan, or a Bostonian, or a Jamaican, or pretty much any English speaker?
Yet another: can you pick out Bob Marley’s accent in his songs?
I missed the 5-minute Edit deadline. So I’ll add:
Depends on the song, I’d wager … I don’t know Coldplay’s catalog very well. But in the Coldplay I have heard (the radio hits like “Clocks” and “Yellow”), the singer sounds very distinctly British.
What’s the average listener, anyway? How familiar is the average listener with various English accents? With modern media, I’d think the average listener can discern this stuff better than you might expect.
All that said, there are loads of cases in which a singer puts on some “other than their own” accent when performing. British singers have done/do it, Australians, Canadians … and, yes, Americans, too (see early Green Day). The change in accent a lot like putting on a different coat and hat and adopting a different persona.
I’m always slightly taken aback when Mick Jagger sings “Ruby Tuesday” and *doesn’t *sing it “Toos-day”.