Passed my driving test!!Watch
You can drive on your own without the physical licence, but if you're relying on the hire car, then yes, they do require seeing the licence. It might be worth giving the hire company a call, because I know when the licence was in two parts, if you'd forgotten the paper part, the rental company could phone DVLA and confirm, at a cost of £10. I don't know if the same applies to the main part.