Anytime (well a few years now) I’ve had to hire a van/car I’ve always had to supply the hire company with a licence checker code, most ask for it to be emailed to them 24hours in advance. Simple to do, takes a few minutes and valid for 21days.
Link I was sent a couple months back (van hire)
https://www.gov.uk/view-driving-licence
motability courtesy car wise all I’ve ever had to do is show identification and they’ve checked paper work to confirm I’m named on the insurance of ingoing car, then they hand over the keys.