Espionage against your home country is considered treason by every single country on the planet as far as I know. That is a capital offense in every single country that I am aware of. As such, if the guy spied on his own country, and he is found guilty, then killing him would be a judicial killing. If he is killed without being found guilty via due process, then it is extra judicial.
Many countries have done it publicly as a judicial killing, and who knows how many have been done silently as an extra-judicial killing. My question was regarding the legality of killing a "double agent" or however you want to phrase it, on foreign soil, in this case England. The question of legality doesn't even have to pertain to this incident. It could pertain to ANY judicial, or extra judicial killing of an accused spy on foreign soil.