http://en.wikipedia.org/wiki/British_nationality_law#Renunciation_and_resumption_of_British_nationality

Also says :-

Since the British Nationality Act of 1948, there is in general no restriction, in United Kingdom law, on a British national being a citizen of another country as well. So, if a British national acquires another nationality, they will not automatically lose British nationality. Similarly, a person does not need to give up any other nationality when they become British.

Different rules apply in the cases of British protected persons and certain British subjects



The thing which confuses the issue is the status of the 'British Person' (British citizen, British protected person, British subject, Citizen of the United Kingdom and Colonies, etc). Thus 'British, born and bred' no problems.