I've heard David Boreanaz's Irish accent was pretty bad during some of his flashbacks on Angel. Personally, I don't think it's that bad but what would I know.
Terrible.

Wait, Linus Roache is English? Wow. He's good.
Yes, he's the son of William Roache, who is the UK's longest-serving soap opera actor, having played the character Ken Barlow in ITV's Coronation Street since 1960. Linus played Ken's son Peter Barlow as a child, and recently returned briefly as Ken's other long-lost son during a break in L&O filming.
[YT]http://www.youtube.com/watch?v=AyxO3M_7C2M[/YT]
And Anthony la Paglia in Frasier
Not only a terrible attempt at a Cockney accent, but the character is supposed to be from Manchester... The worst Frasier example is guest star Scott Atkinson in the Season 4 premiere "The Two Mrs Cranes", as Daphne's ex-fiancé Clive. He'd clearly been studying Dick Van Dyke.
What, her Mancunian natural accent?
No, her bad, fake Mancunian accent. Jane Leeves is from East Grinstead.