Since the temp difference hall/living room is not goig to be great , the absolute efficiency of the insulation is less important.
I'd use fibre-wool. Hugely cheaper than PIR board, can be pushed around to seal any small gaps that might otherwise allow draughts and provides some acoustic insulation too.
... the living room has 2 radiators but the hallway, all the way to upstairs does not have any radiators at all. So the living room is rarely warm as the heat escapes to the hallway and toward upstairs.
I suspect Hillwalker is refering to the fibre-wool normally used in loft insulation.
I'd also consider moving one of the radiators into the hallway. One rad, depending on size, boiler, etc, should be sufficient for the living room.
Otherwise you're either going to have a very cold hallway/stairs/landing and/or you're going to be moving the problem up the stairs to the landing. With TVRs on the rads you could keep the hallway at a lower setting than the living room.
And don't forget to do any first-fix electrics before p/boarding the wall both sides.
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