The Beatles were from Liverpool! I'd imagine you'd recognise that accent. Sooo distinctive! Or maybe Sporty Spice from the Spice girls? I would also say that for locals from a particular region would be able to distinguish the town or part you are from too as there's quirks in language and rhythm. Bex and I would sound very different when we are talking. They'd be words and sounds we'd say differently even if we have quite mellowed accents from working in professional environments. I'm described as a 'posh cockney'. My Dad was a true cockney and my family were mostly from south London. To my ears Essex is a very different accent to south or north London, but I guess there would be a lot of people that would group us together. I very often get mistaken for having an Australian twang as I naturally finish my sentences on high notes and there is a rhythm to the way I speak, but I tend to pronounce most of my letters correctly. The easiest way to tell the difference in which side of the river in London they're from is to ask them to say South London. If thy are from the south (like me), they'll say Saafe and probably Landon. 
The Home Counties (the areas about an hours train ride into the London that surround the city). are probably the most difficult to pinpoint as they tend to be the fairly consistent, middle-higher class accent, similar (though not always as posh) as the BBC news presenters. It's those areas that classes make the difference to a person's accent. Everywhere else a higher class tends to soften the regional accent
The Home Counties (the areas about an hours train ride into the London that surround the city). are probably the most difficult to pinpoint as they tend to be the fairly consistent, middle-higher class accent, similar (though not always as posh) as the BBC news presenters. It's those areas that classes make the difference to a person's accent. Everywhere else a higher class tends to soften the regional accent
Progress is being made!
