Home DIY

You can do it. Downside is you lose useable area in the room. Rigid insulation board probably better than floppy loft stuff. You want to try and prevent water vapour getting into the frame/ onto the wall though, otherwise you will get condensation against the cold wall and hidden mould. Foil-backed insulation board is a thing intended to make vapour resistance easier. Tape the joints.

I've done it - although my walls are cross bonded, not cavity.

I used rough sawn 2x2 for the frame, with 2 inch standoffs to the wall (because damp), fleece insulation held up by battens, and vapour panel plasterboard.

I also added airbricks through the external wall for ventilating the void behind the stud.

If your walls are cavity, and you have no damp, you probably don't need the ventilation. You should probably have a vapour membrane though, because of sweaty breathing kids.

Is there plasterboard against the wall already? If there is, you could strip that, batten the wall, and attach filed & insulated plasterboard to that.

Have used kingspan or celotex in a flat that was badly insulated and had gas supply issues so heating was an issue. Then drylined the flat.