A note of caution. If you remove the stack right the way up through (and assuming there are two stacks) movement may result in the front stack. It is a strucutrual alteration and will therefore require building regulation approval. You will also, as blaccat confirms, need to serve notices on your neighbours under the Party Wall etc Act 1996. This will be a party wall notices.
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The following link provides a tool which calculates the cost of removing 1 or more chimney breastsGoogle "chimneybreast.co.uk" and/or an outside chimney stack.
I think these costs are specific to the company running the site, but nevertheless it gives you an idea of how much the job will cost. I guess this will be helpful like myself you have no idea how much this job should cost
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