YANBU - of course you are English.
But not everyone born and raised in the UK knows what the national terms mean. I remember asking my parents, as a child, what the difference between English and British was and which I was. They told me that I was British and not English because only those whose parents had both been born in England and had been born there themselves could be English. They told me British was the term for people like me, born in England but not to English parents.
I believed that for years. It was only later that I realised British actually referred to a wider definition, covering all the nations of the UK.
I think, for my parents, there was a hangover from colonialism and the Commonwealth when notions of Britishness were being redefined- 'British' had also referred to anyone born in a British colonial territory and then, for a while, a Commonwealth nation. That had changed by the time I was born but was clearly still a legacy for my parents. My family were British, Commonwealth, and X (The nation my parents were from) and that applied to us kids as well. As we were all British, they'd never really thought about whether their children were English until I asked.
Of course all of that is part of a very radicalised and racist history. And one that many modern racists are completely unaware of. For some the legacy of that thinking is theirs still, even though they have no idea were it came from. For others, they are just out and out racists!
As an aside, there's also research though that shows English ethnic minorities are more likely to call themselves British than Welsh and Scottish ethnic minorities (I'm not sure about NI). Theories about that are basically to do with the right-wing and racism so associated with English nationalism.