It's 'arsed'. 'Asked' is a mishearing, retrospectively justified by people saying it 'makes more sense' because you don't want to be 'asked' to do it, which is nonsense. 'Arsed' is slang for 'bothered', which is obviously what it means here.
How can you tell the difference between asked and arsed in an Essex/SE London accent? Just arsking!
You can tell the difference between asked and arsed in any accent, I'd have thought, because 'asked' has a 'k' sound in it. Essex and London accents may drop 't', but I've never heard of them dropping a 'k'!