Besides being mostly sun loving plants, lots of rock garden plants are low users of water and nutrients, so I would suggest you search for alpines that can tolerate a little shade and are drought tolerant and do well in poorer soils, since the trees will tend to steal nutrients. Or you could add cow manure or composted leaf mulch as needed.

http://home.howstuffworks.com/rock-garden-plants.htm

Here is a link that might be useful: Stepables

Believe it or not, tree roots can have its advantages. Soil dries quicker, and I'm guessing that will be an advantage in the UK. Even here in the USA, we have native plants that seem to always do better when grown in an area invaded by roots that are not their own. Of course, growth of the alpines will be slower, but that has the trade-off (usually) of more winter hardy plants. In the UK especially, winter wet is a serious problem, and any evergreen tree will help with that problem, helping to dry out the soil.