I'd say either 'I was born and bred in London' or 'I'm London born and bred' (as a complete set phrase). If the person still lives in London now, they'd be more likely to say the second - in the sense of 'I'm a true Londoner.' To be honest, I wouldn't worry about this phrase, and I certainly wouldn't see it as a grammatical mistake. Yes, the idea of 'I'm born..' does seem strange when viewed in isolation, but old-fashioned set phrases - like 'born and bred' - often do produce some odd constructions.

The word 'bred' refers to animals everywhere, Janeese - not just America. The expression 'born and bred' is a set phrase. It was used in America in the past, but has fallen out of use.

I'd say born and raised. In America we use the word bred referring to animals.

It would be more correct to say I was born and bred because you are referring to an event that has already occurred.

I don't know about Britain, but in America we say "Born and raised." "I'm born" by itself sounds strange since it's something that happened in the past. I would say "I 'was' born in London." My guess it that it is most likely a British Expression.