In a hire car I have a copy of the ID page from my passport laminated and reduced to credit card size, I also have a laminated copy of my driving licence.
I've been stopped twice whilst in my own car, one for a random road side check and once when I was involved in an accident
On both occasions they had a list of documents they wanted to see, they did not bat an eyelid when I gave them the copies
Regards all
John
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