Costs are very variable - sounds a bit steep to me, but I know people who have paid far more around me.

As a basic guide to material costs

£30/meter for the liner
£50 each end for cowl/adapter fitting
£50 register plate

Then possible building work for opening, vitreous pipes, insulation? scaffold?

adds up quite quickly

There are different grades of stainless for liners. The two common ones are 316 and 904. 904 is thicker and a bit more expensive. As liners are usually twin wall you can get combinations, for example 904 inside 316 outside. 904 liners seem to be around £33 a meter on ebay.

£1200 probably reasonable. I generally struggle to do it for less than £1000 with a 904 liner. Does not incl register plate or commissioning of stove.

Open fire places (are there many left??) can not get shut down for a slow burn. Put in a wood burner sooner or later, or as a way of life, it will be shut down for a slow / extended burn which will promote the production of condensate in the chimney. Without a liner this will settle out on the brick work of the chimney soak into the bricks and mortar and eventually come out on the plaster of the chimney breast - typically upstairs where it will stain and smell and be virtually impossible to remove (replace the plaster and more will soak through from the bricks, and the smell will come through dry lining). Whilst you should not slow burn wood stoves it happens and a liner prevents staining coming through the chimney walls and makes the chimney easier to clean. There are probably other reasons as well............

You don't _need_ a flue liner, but the risk is what Peter said. I've had wood burner in two houses. One was fine for 7 years, the other got a brown-stained chimney breast upstairs after 4 years, so I lined it. It's quieter without a liner (chimney alone was silent, with liner you get a faint rushing noise), but it should draw better with a liner.