There is no question whether chimney insulation or liner makes your chimney work better than a non-insulated or lined chimney. However it is often debated whether you will see a return on the money you spent on chimney insulation.
If you have an external chimney breast that is exposed on three sides and the void running through the chimney is quite large, then you will get a lot of cold air trapped inside it. If you connect a stove to the bottom of the chimney, the hot gasses rising from the fire below will be hit by dense cold air sitting in the chimney, slowing these hot gases down as they rise. The result is that it will take longer for you stove to get to temperature as it cannot clear the hot gasses out of it fast enough. This can lead to smoke coming back into the room.
Chimney insulation vs external chimney
In this example a liner will help. The metal of the liner will heat up from the hot gasses rising, clearing the denser cold air trapped inside. There could still be a lot of trapped cold air around the liner depending on the chimney void. Chimney insulation such as a blanket or vermiculite granules around the liner will help to fill the air gaps. This will mean less space for cold air to be trapped.
When stove is lit in a lined and insulated chimney,the cold air will only be trapped inside the liner (typically 6″ in diameter). The heat from the gasses heat the metal as they rise, warming the flue and making it easier to heat the cold dense air. The insulation prevents heat loss from the metal liner, keeping more heat in the chimney. The hot gasses get to the top faster, getting your stove up to temperature quicker. This also minimises the chance of smoke coming back into the room.
Chimney insulation vs 1″ gap
Second example: a chimney in the middle of a house or between two houses in a semi-detached property. If that chimney has a 8″ cross sectional diameter, and your appliance has a 6″ outlet, you will be left with a 1″ gap between the liner and the chimney walls.
While there is enough space to get a blanket or some vermiculite down, the benefit will not be as great. It is hard for cold air to be trapped inside the chimney due to the minimal space. As there is warmth coming from all sides the chimney, it will be much warmer. Chimney insulation is probably not required in this example.
So in conclusion, we recommend chimney insulation. The benefits out weigh the costs and you will enjoy a warmer, safer fire as a result.