Can dry lining be installed over brick walls?

Yes — that's exactly what dot-and-dab exists for, and it is the everyday fix in Maidstone's solid-walled housing. The substrate has to meet a few conditions first:

• Sound: brick or block in good condition, no spalling faces, no frost-damaged mortar
• Dry: moisture meter reading under about 5% WME (Wood Moisture Equivalent) on plasterboard scale — higher and the dab adhesive won't cure properly
• Reasonably flat: out-of-plane deviation under about 15mm over a 2m straight edge; anything worse and we either dub out with adhesive or switch to independent stud
• Clean: no bitumen, no flaking paint, no wallpaper paste residue, no loose render

Walls we refuse to dot-and-dab:

• Active rising damp — fix the DPC first (chemical injection at 150mm above ground level is the standard Maidstone treatment)
• Penetrating damp from failed pointing, gutters, or render — repair externally, allow to dry, then line
• Walls with gypsum plaster already on them in poor condition — old plaster must be hacked off to expose the brick, otherwise the new board is bonded to a failing layer
• Painted walls — gloss and most emulsions defeat the dab bond. We either mechanically key the surface or strip the paint

For Maidstone's 9-inch Victorian solid brick walls (Bearsted, Loose, Maidstone central, parts of Staplehurst), the standard upgrade is 50–80mm insulated plasterboard dot-and-dabbed on the inside. For walls that won't pass the conditions above, an independent metal stud frame with a clean cavity is the more reliable — and ultimately cheaper — option.