You could just build a 240 wide timber frame on top of your cavity walls, rather than the typical 100 or 125 wide timber frame, then 12mm OSB + breather membrane + your vertical battens + your horizontal battens + cladding. Though stopping the cladding at 2ft above ground is a bit odd. Add a nice layer of 25mm Celotex + plasterboard all over the inside if you wish, that'd give you a service void behind the plasterboard too.