Oh, yes, Ken in Dead Again is brilliant (and one of my fave films). I'd forgotten about that, whereas his accent in Wild Wild West and some others is more than painfully bad.
You're right, Albert Finney can get away with anything just because he's Albert Finney. Had forgotten about Cox, but I think he manages it better than some.
What's also interesting is to hear actual Americans on UK programs speaking with American accents and sounding "off". There's a particular cadence that a lot of them pick up which makes them sound like they're faking it. I remember seeing people complaining about John Barrowman's accent on Dr Who/Torchwood when he's moved to the US at the age of 8 and didn't go back to the UK until he was in his 20s...