Flue down chimney work cost me £400, but included pointing my side of the chimney and him knocking out my fireplace (was simple). Building materials for that might have been another £85 in chimney pot, cowl, sand, cement. I think the cowl alone was about £36. 3 storey house so, I bought 12m of 6″ 316 flexi flue (only intend to burn wood so was told 316 would be fine), nose cone, top plate and clamp which came to about £250 from flexifluedirect.
For reference, same builder knocked out an old lintel in my kitchen and put a new one in higher up, cost me £375, but didn’t include any plastering (insurance co are doing that), so for plastering you might be looking at another £300.
Fitting the stove, someone else will have more idea as I’m not there yet. I’m budgeting £500 labour + £150 for pipe, adapter, clamp, register plate.
So around £2000 would be my guesstimate.
I’d take professional advice about the oak lintel, 4″ from stove pipe might be acceptable.