What delivery service or courier service do Apple use in the U.K.?

As we are all users here just like you, we would not know which methods/carriers Apple uses; they also may change those options if they feel another carrier might be better. So, the best way to find out is to ask Apple. Here is the general shipping info for the UK store:

http://www.apple.com/uk/shop/help/shipping_delivery

In my experience when purchasing from Apple Store UK, in the last 8 months I've had DPD, UPS deliveries. But I'm certain there is more.