Detritis (crap) falling into living room

I have had this fire in place for 14 years, recently the coals on fire have been subjected to detritus (stuff) coming down the chimney flume and falling into the fire, and often then into the living room. I also have an open fireplace in the above bedroom which blackened bits of stuff fall from. The upstairs fire has not been touched since 1940's and is never used, the downstairs has a gas powered fake coaled fire that is used occasionally. If needed what do I d about reinforcing themI'm not sure this is problem but on a DIY show years ago they put a metal tube through top of chimney to bottom and then filled the excess area outside of this with concrete. Is this evenstill the right thing to do or have I dreamt this, If not a dream, who could do it and at what cost?

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