The house wall as built was standard cavity wall, brick outer, brick inner, 65mm cavity. U=1.7. Sometime around 2000 the cavity was filled with blown fibreglass, making it nominally U=0.49. I added 100mm PUR (Polyurethane) foil-backed boards with plasterboard on top, to get to U=0.16.
The main risk of IWI is that if it is not well-airtightened, wet air from the building can move behind it making the wall soggy and promoting mould growth. So it's important to get the detailing right - seams taped between boards, boards sealed to walls and floor and joists. I used separate insulation and board rather than the pre-bonded ones you can buy for this reason. If the plasterboard is already glued to the front then you can't seal the joints in a vapour-proof way between each board. It's much better to put up the insulation, seal it all up, put in any services or mounting points for heavy things like radiators, and then glue plasterboard on top.
I took evidence from a chap who'd done a superhome and fitted PUR in this way in a bathroom, then over a decade later pulled it off to see if the wall behind had suppered from mould at all - nope, all lovely.
Another vital thing to do is not just ignore the section of wall between downstairs ceiling and upstairs floor. This is very likely to be the worst bit of your wall. Mine was unplastered, so much less airtight, with big holes like half-bricks missing in various places for wiring to come through out of the cavity, and gaps around the joists, which are sat in the wall. I didn't appreciate this on my first house so just missed this bit out.
Cavity wall insulation is a good thing, as it's cheap and a major improvement, but it should be noted that it is unlikely to produce the theoretical U-value due to voids blockages and detritus in the cavity. We had a lot of places where the insulation was compromised. The most egregious was the right hand half of the front wall, which had a large clematis growing up a trellis. I noticed there were no cemented-up injection holes here, and indeed, upon inspection it had simply not been filled at all (presumably the installers couldn't be arsed to fight through the plant and thought no-one would notice: they were right for at least a decade). I was able to use the guarantee to get the installers to come back, confirm this and actually do it properly
I found voids every time a section of cavity was revealed, e.g. around windows and doors. Sections at the corners of the house also had large gaps. The wiring was originally done in the cavity, and that had blocked flow, so there were often gaps where wires went too. The bottom 100-300 mm was full of cement and dropped bits of brick/tile so no insulation there either. Finally a thermal survey noted that a lot of heat was being lost at the bathroom vent. TUrns out that a) there was no pipe through the cavity, just a vent into it and b) there was no insulation above the vent so the bathroom warm air just spread up inside the cavity. I stuffed some fluff in here and removed the vent, to replace with MVHR (eventually).