Yep stumbled upon an interesting one here, ID when renting a car can be a little bit of a minefield, in the UK they have started been quite strict on what ID is required from UK residents, you are required to prove your address, but quite often an address check will be performed upon pick up, if the drivers is not actually registered as living at the address (not on the electrol role) like I say little bit of a minefield, but for sure each and every person whom books with us is made aware of what they need upon arrival to ensure they collect their hire car without a hitch.
Re this specific question I can only assume this is for a visitor to the UK, as if collecting the vehicle as a UK resident you only require both parts of your license and a proof/s of address.
If arriving from overseas you are required to present both parts of your drivers license (if a UK license) or your full license (for example full EU / US / AU) in some cases suppliers will require to see the hirers return flights details, so again can be a little tricky if you are on a one way ticket, which some people are for a variety of reason, and none of these reasons are to steal a hire car
Whilst not 100% sure about the initial inquiry, I figure this is from someone whom is flying in from a EU member state, who does not have a passport, just a European ID card, and in this case the advice the best way to look at it is ‘If it is good enough for UK passport control, it is good enough for a car rental company’
If we can package this information up in the form of a blog it would no doubt service as useful information for people.