I have heard of the mythical few that have quoted EU Law (along the lines of you only have to give as much notice as the frequency you are paid ie a month) but I think the QR which talks of "extingencies (sp?!) of the Service" has primacy. That said, if you have a guaranteed offer of employment to go to, which can't be held open, or indeed a genuine need to leave HM employ straight away (family illness etc) raising the question formally with PMA, through the chain of command, has been known to work. May affect any pension / gratuity benefits so take advice from the relevant Pensions people first. Personally, I think its better to work out your ticket and leave the Service on "good terms" (particularly with your Boss!) than employ a solicitor (which will probably only save you a few months at best) and leave with a huge bill in your back pocket!
Best of luck with whatever your future holds.