OK, so if you don't mind, let's take your family as a good example of what I'm saying, and let's further posit a world where Britain completely halts all immigration today, so from some near future point, every child born in Britain is born of British-born parents. Now let's suppose that you have children, and that they remain in Britain, marry locals, and have children of their own, onwards forever, never leaving the country except for holidays.

Since, as you say, your hypothetical children would not be purely British, at what point are your descendents 'pure Brits'? Is it 50 years from now? 100? 500? Now think about what life was like in Britain 50, 100 and 500 years ago. How close would you say the lives of children today are, compared to children in those times? Closer than to children born today in, say, Norway? Consider that 1986 is as far away from today as it was from 1946; someone born today is as distant from someone born in the 80's, as someone born in the 80's was from the end of World War 2.

And think about British culture in the 90's and 00's - it was heavily influenced by US culture at that time; today I imagine things like K-Pop are having an increasing influence. Britain (as indeed most other nations) has for thousands of years been a melting pot of different cultural inputs. In fact, the very notion of 'Britain' has changed over time - the British empire once spanned the globe and included places as diverse as India, South Africa and Singapore. Even the Britain of today is not a single country; would you say that, say, Northern Irish and south-eastern English people are culturally homogeneous?

So, while I do agree that telling me you were born in Britain, or China, or Zimbabwe would help me to calibrate broad expectations about you, I can't see how any of those things is or ever was 'pure' in any way.