The UK sits at a latitude where global atmospheric circulation cells converge namely the Ferrel and Polar cells. Where the convergence occurs high in the troposphere, the cells give rise to the Jetstream. Together with the Earths rotation, axis of tilt and orbital path around the sun, they produce circulating weather systems of high and low pressure.
As a result, the UK is bombed by low pressure systems where moisture is picked up over the Atlantic and when the air hits the UK coastline, the air is forced to rise. Pressure drops and the air cannot hold the moisture so it condenses out and falls as rain. The cold is a function of more northerly air streams on the trailing edge of low pressure systems pulling down colder air from polar latitudes over the UK as they move from west/south west to east/north east.
All this to say, any given weather system cannot be 100% attributed to global warming. However, the frequency and severity of these weather systems are increasing and this effect can definitely be attributed to global warming trends.
If the trends become established of a period of decades, then yes, the UK climate is changing. i.e. Global warming is changing the UK climate to bring extremes of weather events.