A cold lifeless place in the dead centre of hospital (6)

I believe the answer is:

morgue

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'hospital' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for morgue that I've seen before include "room kept cold!" , "Our Meg (anag)" , "The Murders in the Rue -- (Poe)" , "Building for conducting postmortems" , "Place where dead bodies are kept temporarily" .)

I've seen this clue in the Irish Times and the Irish Times (Crosaire).

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