Or an ethnic minority, for example Mo Farah or Archie Panjabi. As far as I can make out, minorities preferred "British-x" (e.g. British-Asian) as a label rather than English even if they were born in England, although there have been calls for that to change [1].

[1] https://www.theguardian.com/commentisfree/2010/jun/23/englis...