I am looking for advice as to how best we should proceed with what has got to be one of the most oversized domestic chimneys in Kent. We've known for a while that the render (sand and cement

I had a look on the weekend and the flaunching is indeed a real mess as you can see. The render is cracked in places and it's obvious that the bricks at the top are completely saturated.
What are your thoughts on how best to proceed? We were hoping that we could remove the render and re-render in lime once it has a chance to dry out but the builder we're working with has said that he's worried that removing the render will remove any structural integrity the chimney has and has suggested taking it down.
We would like to be able to install a wood burning stove and be able to be able (occasionally at least) to use one of the open fires but this is now looking increasingly unlikely.
As always I would welcome any advice.
Many thanks.
Scott