I had an emergency situation last week - realised DS's passport was going to expire whilst out of the UK. Dire warnings all over passport application site that applications are taking longer during peak periods, no one day premium slots for another 2 weeks...
Well, there is an agent in London who has slots on hold each day - if you can get the paperwork to them you can get the passport in a day or two
NB: i don't work for them or earn commission!
But if you are stuck and can pay the fee, it might be worth getting in touch with Benmar. Cheaper than a holiday cancellation!
Good luck all