From experience, I would be surprised if the chimney in a victorian flat didn't need lined.
When wrightyson talks of 'failed stoves' 'm guessing they were fitted into an unlined chimney but then smoked back/ran badly/leaked.
If your flat is part of a bigger vuctorian building I'm guessing your flue is part of a stack containing, lets say 4 flues in total.
4 flue stack= tonnes of masonry.
In victorian times 4 open fires runing almost constantly might have had an output of 12kw each but at least 9 of those were going up the chimney. So 36kw of heat warming the stack makes for a healthy draw.
You open your fireplace now and put in a 5kw stove which puts 4kw to the room and 1kw up the chimney may never warm the flue enough to get a good draw. Lining is by no means essential but is certainly a good idea if you want peace of mind your stove is working as best it can, is easy to sweep and isn't gassing your neighbours through the wall.
*I am not a purveyor of chimney liners, but I do fit plenty*
To the original question - I would reckon around a grand for fitting and the same again for lining with top grade liner. Don't get cheap and nasty stuff, it's really not worth it.
Do it, you will love it. I've put quite a few in old places like yours and they heat the fabric of the building in a way a radiator never can. And sitting in front of it with a book and a dram is sublime.
As others have said, don't go too big - a 5kw stove chucks out a lot of heat. I fitted 2 stoves to this big victorian house at 7kw each, one in each end (the huge rooms with the bay/hex windows and they pretty near heat the whole place as the heat goes out into the big hall and upstairs. Proprietar is delighted with them.
Is that you only source of heat?
