Firstly, assuming that you hold a UK passport, there are two fast-track processes available to you. ('One week' and 'one day'). So you can get a passport with plenty of time to spare:
http://www.direct.gov...pplications/DG_174149
My own passport is covered in coffee stains (including the photo page). It's been given some odd looks by passport officials but I've had no real problems with entering or leaving the UK, France, Belgium, Germany, Italy and Slovakia with it.
So you might be OK to travel with your existing passport but it would seem to be unwise to take the risk.
Chris