Chimney re-lining recommendations

Hi,

We have a downstairs and upstairs fireplace (same chimney stack, upstairs not used), and get quite heavy smell of smoke (but no real visual smoke) in the upstairs room when we light a fire downstairs.
Have therefore stopped making a fire, and want to get that fixed.
The house is a mid-50'ies standard mid-terrace 3-bed old council house.

I guess I want something like those stainless steel tubes and hood fitted, and backfilled with fire-proof material. In addition, I'd say that the innerts of fireplace itself needs replacement (in case the walls are cracked).

Hence looking for recommendations for a Chimney re-lining company. I don't have a budget yet hence also looking for price indications.

Appreciate any input.

Thanks
N

A work colleague had his done today by Tim Qunilan of Templemore Chimneys. Had to leave a window all the time to get the fire to light without the room filling with smoke, he lined the chimney with flue liners & fitted a wood burning stove to the opening. My parents had a chimney rebuilt by him a few yrs ago & I had a chimney lined in an investment property, my insurance company recommended him. Very nice guy to deal with. I can post a number tomorrow if needed.