My daughter was born in the US and traveled on her US Passport, but from my understanding she may have dual citizenship?
The only people who are now considered British ‘subjects’ in technical terms are Irish citizens born before 1949(when Ireland became a republic), which has very little significance, other than the fact that an Irishman or Woman born before then has the right to style themselves ‘Sir’ or ‘Dame’ if they receive a UK Knighthood (e.g. Sir Terry Wogan).
Everyone else has been a citizen since 1983 when the British Nationality Act of 1981 came into force. Before then, pretty much anyone who had the Queen as the Head of State was considered a British ‘subject’ as well as a citizen of their respective country.