Is the car in the original post now off the table?
How much service history is missing?
The seller states "Complete with an almost full main dealer (printed) & specialist service history"
Doesn't sound like much is missing and if the recent history stacks up I don't see too much problem.
Id still try and get the price reduced for the inevitable bits that will need fixing.
Everything said is immaterial. The OP has paid a deposit and it collecting the car soon. Nice enough car, but not 'rare' or likely to 'rise in value' any time soon as advocated by the seller. OP, pick the thing up and enjoy it.