What about a
complete cock? I would say that's gender-specific.
I would call a bloke a complete cock, but it wouldn't occur to me to call a woman one. Likewise, dickhead.
There does seem to be somewhat of a gender imbalance here though.
I would use twat, cunt, cock, dickhead for men, but for women the only one I would use (and as a woman they'd have to piss me off a lot more to use that language) would be cunt.
Maybe chivalry's not dead after all?