Had this done a few years back and it came to a couple of grand I think but that included the fire.
There are a few points here.
Firstly if it's a large fireplace there is a ratio of the opening to the flue diameter that you need to have for the building regs. So if it's a larger fire place like ours was you need quite a wide diameter lining.
The twited nature of ours (the cottage is about 300 years old) meant that a rigid lining couldn't be used and the construction of the house meant that they couldn't use a cement lining system so we had to have a flexible lining. That limited the opening so we had to have a stove but there are some by Dovre which are basically like an enclosed fireplace that you can open up.
The working at heights directive means that you need scaffolding up to do the job so that has to be budgeted for - no more dangling off of ladders!
And you need sufficient ventillation so you might need an air brick - a reputable chimney company are likely to insist on this if they are doing any work for you.
All the details on sizes etc are in here:
http://www.planningportal.gov.uk/uploads/br/BR _PDF_ADJ_2002.pdf
Looks a bit scarey at first but most of it won't apply to you