My passport has expired and I didn't know!

I'm due to travel next Saturday and I've just realised my passport has expired. The expiry date is not for another 9 months but it was issued over 10 years ago, so is invalid. I can't get an appointment at any passport office next week for an urgent renewal and I can't cancel my holiday. I waited all day for the passport office to phone back, which they did and then promptly hung up! I finally managed to 'webchat' with someone who told me that if there were no appointments showing online, then that was it! Has anyone else had a similar experience or can offer any advice? It seems unfair especially as the passport office are still charging for a premium service when that service doesn't really exist!