Probably by the Sea Viper system from a destroyer parked in the Dover Strait. Now, the UK probably doesn't have enough interceptors or destroyers carrying them to be confident they'll be able to stop a proper all out attack, but that seems to be a common problem with every Western country right now with a peacetime military budget in an increasingly unpeaceful time.

Sea Viper can defend against short / medium-range BMs impacting in its vicinity, not IRBMs passing overhead in mid-course to a distant target.