A bit of background: I've bought a house built in the 1960s which has been retrofitted with "bolt-on" insulation. On the inside, which was done first, there is a layer of plasterboard with insulation bolted to the brick and plaster walls - in places this was very shoddily done.
On the outside, there is cladding that has been bolted to the outside and rendered with some kind of spray-on roughcast - this was done much more professionally.
Having recently discovered the internal insulation (by trying and failing to fit a shelf) I'm considering removing the internal insulation to both increase space and allow me to more easily fix shelves etc to the walls.
Is this advisable given the external insulation, and does anyone have any data comparing heat loss with internal vs external vs none vs both?
Edit with more info:
Thanks for the answers so far, I will consider carefully before deciding whether to remove or not.
I'm in a wet & windy climate, between 1 and 15 degrees C year-round. Wall construction is brick & plaster (I believe there is a cavity), then 3" thick polystyrene insulation on the outside.
According to another answer I read on here, internal insulation can have the effect of keeping the brick walls "cold" by reflecting the heat back into the room. This has the effect of stopping heat leaking out, but when the heating is off, it gets cold very quickly - this has been my experience so far. Considering I have external insulation, I could remove the internal, and lose a bit of heat to the walls but warm them up, helping to keep the rooms warmer for longer rather than warm / cold immediately. The external insulation will stop this heat loss being extreme.