Driving abroad on old license

I moved house a couple of months back, and have since gone on a fairly long business trip (a few weeks long).

While abroad, I realised I needed a new license with the address updated, and ordered it from the DVLA. That new license is now sitting in the postbox at home. Bit of context -- I don't own a car and only drive occasionally, which is why it took me a bit of time to realise I needed to do this.

Anyway, am I right in thinking that I cannot rent a car while I'm abroad using the old license that I have with me? Nothing else has changed, driving license number/photo/etc all as before, no points or offences, but the address it shows is no longer valid.