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.

A missile would need to fly all the way over Europe before reaching London. It would be noticed, jets would be scrambled and it would be shot. Just like what happened here.

These were ballistic missiles. They are only vulnerable during the terminal phase, when they are moving at hypersonic speeds. Standard fighter jets aren't going to do it. It would take ground based THAAD, Patriot, or ship based Aegis systems. London might want to budget for that.

or take (less) of these https://en.wikipedia.org/wiki/SAMP/T 8^)

They can fly well above any commercial and military aircraft.