No they can't, they can be a British Citizen/Passport holder that isn't the same thing.
If I go to China with my wife and we have a child, would that child be Chinese? Can I be African or Indian? No no no.
This is why these questions of Britishness are so utterly pointless, if we cannot give the answer than makes the most sense then it doesn't mean anything.
If you and your wife moved to china and while living there had a kid then he would be chinese .
I doubt any Chinese person would take that seriously
so there is no such thing as white Americans or white australians