You can get a stainless steel twinwall flue that will go out of the wall and up the gable but it will be expensive. Stove fitters may not give you the best advice on flues so the best thing you can do at this stage is make friends with your local chimney sweep, who will advise you and set it all up correctly, making provision for himself with a port for when he comes to sweep it in future years. He’s counting on repeat business so has an interest in doing it right.
Edit: an old isolation hospital would have been built when coal was cheap and no consideration was given to insulation.
If you are refurbishing an old house, give strong consideration to dry-lining all the exterior walls with modern insulating materials. It will cost but will give you more freedom with electrics and will save you an absolute fortune in heating, as well as making the house quieter and generally warmer and less drafty. Also you won’t need to worry about the old plaster or anybody else’s crap wallpaper. At the same time I would consider pulling down all the upstairs ceilings, re-wiring for modern lighting and putting up thick Kingspan then re-boarding and skimming.
