My family have, as far as I know, always been British and I have family connections with North America and Africa rather than Europe. However, some of my dearest friends are European. We share similar values and a common history.
When the United Kingdom joined the Common Market, nobody ever wanted to see war in Europe again. Most people still don't. As far as I can tell, nothing has really changed. As more countries join the European Union, our voice has become somewhat depleted but being outside of the European Union will deplete it even further. It's not a good move for us, either economically or to preserve our sovereignty or security. I want to remain both British and European.