What system is there in the UK to prevent collisions between small aircraft?
Small airplanes will be under VFR (Visual Flight Rules) which entails that the pilot looks out the window and is responsible for staying away from other aircraft and staying out of the clouds (the fog banks of the sky). 

If you see another plane in your path then there are standard rules to avoid him see this question.

They can fly under IFR (Instrument Flight Rules) but that requires that Air traffic control monitors the airplane and steers it away from other planes.