You have competition for the worst attempt at a Brit accent!
Scarlett Johannson (yes, I would) sounds as british as a Yankee Kangaroo in The Prestige
Don't get me wrong, some actors aren't exactly phonetically versatile (Sean Connery, Michael Caine)
But Johnny Depp and Renee Zellweger have both managed convincing London accents, and the Spinal Tap boys (especially Harry Shearer who's managed to sound like a hippy brit and now become Ned Flanders/Mr Burns/Apoo etc.) had me convinced they were English.
Brian Cox, Catherine Zeta Jones and Bob Hoskins have done OK the other way (I've spoken to yanquis who thought they were really American actors)
So come on Scarlett. Make a fUckin' effort!