Is the UK that far gone that you need to distinguish that children are being educated in English?
You are aware that English itself is an immigrant language in the UK, and that the language and the country of England are named for their original home in Angeln, which is now in northern Schleswig-Holstein? And that the official languages of England were French and Latin for several centuries after 1066, and English could not be used in courts of law until 1661? And that the current ruling house is German, with Elizabeth II being the first monarch in that house to have any recent English ancestors (on her fathers side, you have to go way, way, way back before you hit an English ancestor).
For the greater part of its history, education in "English medium" would have been considered a fanciful idea in England.