We had a woodburner fitted in our new house back in March. The house is approximately 5 years old and already had a chimney which the previous owners used occasionally with an open fire. We didn't get a liner fitted originally as the chimney seemed OK. However after a few weeks, soot deposits and more importantly tar deposits started to appear on top of the stove. We decided to have the chimney lined as this seals the whole flue and any deposits will come back down inside the stove. It cost us around an extra £500 which included the fitting/transport etc. If you do decide to fit one, it could cost less if you get your chimney sweep to fit one you've sourced independently.
I had a liner fitted and it was bloody expensive. I remember thinking it would only be about 400 quid to instal the logburner but after fitting and lining costs it was closer to 2 grand all in .
Our chimney sweep recommended lining (he was independent of the shop where we bought the burner and independent of the fitter) and we have an old house so I was happy to do for peace of mind, but I was shocked how much it cost.