Not at all. Jutland is a region of Denmark. England is a separate country, along with Wales, Scottland and Northern Ireland. Collectively they form Great Britain/United Kingdom. Granted GB/UK is referred to as a country but it's also referred to as a country made up of four smaller countries.Anyway ask most people from GB/UK and they will say they are either English, Scottish, Welch, or Northen Irish, and not British.
It's more of an individual choice how you view yourself and your background.