In reply to Greenbanks:
There's 10% off used stock at WEX just now, including a Sony RX100 III for about £270 and a Lumix tz100 for about £225 (with discount). Possibly worth a look.
For actual climbing I prefer something with a fixed lens (retracting or similar so you don't have to faff with a lens cap) that can be operated with one hand. I've used a Ricoh GR (16mp apsc model) and rate it for image quality, although battery life suffers in the cold. It also easily fits in a pocket. Pretty sure they can be found dirt cheap on eBay.
Whilst I agree that, viewed on a phone / laptop screen, phones are comparable to 'real cameras' these days (and arguably better than older compacts), I think there is pleasure to be had in the craft of using a real camera. The GR and Fuji equivalents offer more in that regard in my opinion. Phones are great for convenience, but I've never enjoyed using one for photography.
Post edited at 09:01