Hi
The cost to buy only the parts is about �350 (that's to line the chimney, connecting from a wood burner and terminating with a cowl. The cost will depend on the grade of liner you use, length of chimney, type of cowl etc, and also whether you buy from an internet company (type "flue liners" into google) or from a local supplier.
The cost for a professional to do the job (supply and fit) is around the �800 mark. This is the cost that a local company would charge using roof ladders. As terence7556 says, larger companies will use scaffolding and that would increase the cost.
Chimney lining now comes under building control and should only be done by a HETAS approved engineer. This will give you the right documentation if ever you sold your house and maintain any house insurance in the very unlikely event of a claim being made.