I got to Dover on route to the GP at Spa a couple of years ago to be told my passport ran out in Jan, after going to L M with it in June of the same year. Dashed up to passport house getting there 10 mins before it closed at 1600, to be told that I needed proof of travel to have it renewed there and then. Thankfully I had bought a ticket in Dover 2 hrs before hand so they reluctantly renewed it by 1800, dashed back to Dover for the next ferry, and made it to signing on in the Casino at Stavelot with a few hours to spare !!
So you've got loads of time yet !! Best of luck with it anyway!!