Personally, I used to use this sort of thing to keep all the important documents while touring.
www.wilko.com/en-uk/single-wilko-a4-punched-pocket-wallet-in-assorted-styles/p/0348796
Nowadays, just touring in this country, any documents we may neeed are kept in an A4 envelope.
I've always used a A4 envelope/folder (similar to recommended above), and tucked it between front seat and centre console to keep it readily to hand and damage free. On a variety of cars it's always worked well for me.
Make sure the documents are very secure and hidden away. If the vehicle is stolen, they then have the V5 to sell it on to some unsuspecting person. We always kept the V5 in a plastic wallet in the caravan when touring the continent. Just to add we were never asked to produce it and unlikely you will be asked unless in a mishap.