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edit: was also thinking about getting a chimney sweep for good measure
Ah, I can save you money / heartache here
If you do need roofwork and / or chimney work done, you can have the chimney lined as part of the roofwork assuming it hasn't been done already, which given your photos it almost defiantly hasn't. You can get the sweep in at the point just before you have it lined. No point getting them in before then; any roof work or pre-lining sweep will release more.
we’re never going to have a proper fire or stove in there
If that's the case, probably better to just clear out whatever crap is in there at the moment then leave it - sweeping it will just dislodge more stuff for no purpose really. Sweeps - as I have learned, like to work on working appliances. They might take your money for sweeping a non working flue, but they know the work is largely pointless, and even borderline damaging.
sorry, the earthy plaster is with pebbles is on a different wall - all the crap in the chimney was fine and black, not sure whether it’s capped up top or not tbh, still need to find a roofer to get up there
edit: was also thinking about getting a chimney sweep for good measure, even if we’re never going to have a proper fire or stove in there