There's also the simple fact of not feeling a particular attachment or sense of belonging to any one country due to moving around/ mixed nationality parentage and giving your nationality simply as listed on your passport - there's no English/ Welsh/ Scottish passport (yet)
Scottish and Welsh people often have a stronger sense of national identity. I disagree with ContessaLovesTheSunshine and think she has it backwards - though "make British great again" might be a slogan of UKip Brexiter types that's just for the handy pathetic "play" on Great Britain. Your typical xenophob nostalgic for a supposedly great past is more likely to call themselves English.
If people have a sense of regional identity they might identify as a Yorkshireman/ woman, or Cornish, or whatever. England is too populous and bland and has too shameful, unromantic, privileged a history to have the appeal of the strong identity.
People who feel to diluted to claim Scotland or Wales, or no claim on those countries, and no strong sense of English national identity are more likely to say British than English just because meh, that's what's written on the passport imo.