If the flue overhangs the boundary it is trespass. If you do not remove it the neighbour could apply for a court order. Although the court may only grant the order if the infringement is sufficiently serious.
As to the proposed replacement, you should discuss that proposal with a building regs officer to ensure it is compliant with building regs.
The answer to your first question is yes.
Regarding, your second question, I cannot tell you the odds of success, each case is decided on its facts.
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