When I applied for my current job it was pretty much double my previous salary... if you don't ask, you don't get
I've applied for two jobs this week that I'm more than capable of doing that pay £100k+... I had the client for one of them ring me up saying they would love to have me in for an interview, but as my current employer provides them with 'stuff' they have a legal contract with them not to poach staff... I didn't know who the client for the job was until they called, if I'd have known I would have knew it was pointless applying.
You have to apply though... sooner or later you'll get lucky and someone will give you a chance.