I guess it depends on what you mean by English. England is a country, but you can't have an English passport, you can only get a UK passport. so, English is a kinda-sorta a non-nationality, but it is very much an ethnic group.

I don't think anyone is claiming that Rishi Sunak isn't a UK citizen, but he certainly isn't a member of the English ethnic group, or any of the Celtic ethnic groups that also make up the UK's native population.