In reply to The Potato:
It all depends what you're looking to do in them. If you want a pair of shoes that you can clip to your harness to make the walk in/back comfier I'd say there's some really lightweight sportiva ones. (Can't remember the exact name, but i think they're actually lightweight running shoes)
But if you're more into exploring places with grass and mud to slip over on, a pair of fell running shoes might be better, but a bit more extreme (they are ventilated to let water drain out after a stream crossing, but this means they also let water in from the slightest puddle...)
For British winters you want a warm shoe, but then if you don't really climb much outdoors in November to February and take holidays to Spain and such, you would probably prefer something lighter with more airflow and the classic "bobble" rubber on the sole is fine in Spain where there's less grass to slip on...
Basically, not many approach shoes seem designed for wet British grass slopes. Yes, the grippy rubber is quite nice, but then i wouldn't say it's essential. I did manage to follow my mate up croton oil (HVS) in an old pair of nikes and, as others have said, Tom Randall climbed London's Wall in a pair of guide tennies. Pete W did technical master in them too, but then there's a video of Johnny Dawes doing it in Reebok's. It's interesting seeing what you can climb with less technical shoes sometimes (as long as they're clean and you're not scrabbling up the rock) certainly gave me a bit more confidence
Post edited at 08:38