In reply to Zoe Langford: Assuming you mean for the UK as opposed to anything higher/ colder
Don't focus on "waterproof" too much, as one way or other your gloves will probably get soaked anyway and ironically non-waterproof gloves dry out much quicker.
I would suggest going for a "system" of 3 gloves rather than one set of gloves, something like:
You'll probably get quite warm during the walk in. Get some thin liner gloves - silk or meraklon for less than £10 for the walk in and gearing up.
Get some pile lined softshell gloves for climbing in. These are warm when wet, dextrous and dry out quickly. eg Outdoor Reasearch Extravert or Mountain Equipment Randonee (£25-£45)
Keep the windchill off your hands when stopped. Get some shell mitts to bung over the top when belaying eg Decathalon Boost Heat mitts £8 or Buffalo mitts £20
Wrap a drink bottle full of your favourite warm drink in your belay mitts so they're nice and toasty when you stop.
Keeping your hands warm is more than a consideration of gloves - keep hydrated, eat plenty of calories (try hot choc with double cream or butter, eat cheese, salami etc) and keep your core warm and dry and keep moving when stopped.