It is an interesting question , which often leads to a lot of heated debates , but I think if approached with genuine curiosity and open mindedness can be helpful to think about.
I was born in England and have a English accent. I am white, and my family , as far as I am aware , have lived in England for centuries. That said , I have absolutely no connection with Englishness, and frankly , I don't know what it even is meant to be.
I think unless we get a consensus on what Englishness means , the whole argument is relatively pointless. The right wing nationalists would have you believe that to be English means you have to be white. If one solely uses ethnicity and race as a barometer for Englishness, then that is an interesting argument to have.
However, many people in the UK see being born in England is making you just as English as someone who's family has been here for centuries, regardless of skin colour or tone.
I have heard arguments that if a white English couple immigrated had child born in China, that child would not be Chinese. I am unsure how offensive that would be for the English couple.
If we trace our ancestry back , we are all from Africa or thereabouts. It is also ironic that right-wing nationalists, complaining about their culture being taken over, seem to have a blindspot regarding colonialism throughout history. The chickens has come home to roost, and it is hardly surprising that non white people will claim to be English, if England historically colonised their countries.
Personally , I think the whole conversation whilst interesting , is pointless , because we will never get agreement as to what being English actually means. The whole thing is a man-made construct regardless. Humans drew borders and categorised other humans based on what they look like. There is no inherent "English" just as there isnt an inherent "Chinese".
TLDR: interesting interesting topic. However , unlikely to be resolved as everyone has their own unique understanding of ethnicity and nationality , much of which contradicts other people. Nationalists will always use race or ethnicity when it comes to these conversations. Which is ironic as they often don't like race to be mentioned in any other context.