Thanks for all the replies guys. To be fair, we also have 5-6 inches this side of the Severn bridge and my drive has quite a slope on it. Also, I think there was a bit of slush under the top layer of snow, so I had snow sliding on ice, which I guess is a challenge for any kind of rubber.
I bought two sacks of salt grit and cleared clean channels all the way, so I'm going to get the car on the street later and see how it goes. From the comments, it really must be a case of either crap driver or really crap Bristol snow :-)