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.
The usual meaning of English. Say, roughly the criteria that would make someone eligible to play for the England football team. Skin color has nothing to do with it, and I can assure you that very few English people either know or care whether they have any ‘Celtic’ ancestry.
No-one questions the Englishness of white men born in England to two non-English parents. People raising the absurd non-issue of Rishi Sunak’s Englishness are just concealing their rather obvious prejudices with a lot of bafflegab about ‘English ethnicity’ (a concept which not even they can really take at all seriously, if they at least have some acquaintance with English history).
If we go by the explanation from wikipedia [0], Boris Johnson and Nigel Farage would not be considered English, as their families are not part of the English or Celtic ethnic groups. Their ancestors are Turkish and German who came to the UK after 1850. Do you believe they are not English? I mean even the current King of the UK would not be considered English by your definition! He is descended from Greek, Danish and German people [1].
[0] https://en.wikipedia.org/wiki/English_people
[1] https://en.wikipedia.org/wiki/History_of_the_monarchy_of_the...