The thing with chimney removals is that often you don't know what the neighbour on the other side has done, and nor the condition of the wall between the flues.
Reading the comments again it seems the structural engineer employed by the builder has 'taken into consideration ' the neighbour's work to the chimney ,whatever that means. It isn't clear that you or the structural engineer actually know the chimney stack is not properly supported ,and if it isn't how is it standing up ?
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