You are à British citizen, you are British.
English ??...probably not.
You can also claim to be British as you were born and raised in England, but English is not a nationality, British is. If you are a citizen of India then you can say with confidence that you are Indian. If not a citizen, then it's probably more accurate to describe yourself as being of Indian descent.
As you or your parents come from India for you to say you are English would be an insult (just the same as if I were to call you a wog or Paki (no racism intended)), I understand why you consider such words offencive therefore you must understand that trying to steal our identity is just as offencive to the English.
As within Britain I identify myself as English rather than British - I don't relate to Scots or Welsh the way I relate to the English. But then I don't have anything against non-English Britons.
English = born and bred in England.
British = Could be either English, Scottish, Welsh or N. Irish or someone who holds a British passport through entitlement.
I am British English.