At heart, London's thin red line! (7)

I believe the answer is:

central

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'line' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Perhaps you can see a link between them that I can't see?

I can't explain the rest of the clue.

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(Other definitions for central that I've seen before include "Key" , "Near the middle" , "like this answer" , "Most important, principal" , "Focal" .)

I've seen this clue in the Evening Standard.

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