Actually we couldn't. What authority do we have to hold a referendum? Who would hold such a referendum and who could vote in it? There is - legally - no country called England. It exists as a concept, as a past reality, as an emotional concept for a group of people, but it has no legal standing. There is no English parliament, and therefore no authority which exists that we could appeal to in order to exit the United Kingdom.
Its a bit of trivia quiz question, but in fact Scotland is the only country in the United Kingdom. Wales is a principality, Northern Ireland is a province, and England does not exist.