If you have a chimney pot, drop something like this into it...........
https://www.ebay.co.uk/itm/chimney-cowl-terracotta-Kent-Choice/174455485388?hash=item289e5b73cc:g:zRkAAOSwOb5fcdr~
Or if no pot, then bed a large piece of slate or paving slab across the stack. (Bed the four corners but leave a space on the sides for ventilation.
Take out the fire surround, fit a piece of 100mm Celotex insulation board into the opening, plasterboard & plaster.
Fit a new piece of skirting board across the wall, and let a 9x3 inch aluminium vent cover into the skirting.
I'm afraid that ventilation is essential. Using old clothes is tempting, but eventually, the smell of rotting fabric will get to you ;o(