I was thinking of battens and counter battens holding a drained rain screen with the “house wrap” under the battens, so no boards directly attached to the studs. House wrap to run vertical with all joins sandwiched between a stud and a batten. Hence getting a wall that is very vapour open to the outside without needing expensive (and heavy) boards. (But are breathable house wraps strong enough to be used without a backing board – they must be as that is how we use them on roofs!)

There is a Larsen stud based design that have braces within the wall (1by4 timber or metal strapping), that does not need any boards for racking reasons (Sorry I have lost the link to it). I don’t know if such a design will pass UK building control, or if putting OSB on the inside of the frame is cheaper than getting a custom set of calc done!

I assume that with icynene insulation in a breathable wall there is no need for a VCL so plasterboard could be fixed directly to the studs.

''Sorry, I don't understand what you mean by "racking reasons".''

Boards used specifically (or mainly) to resist racking. Not necessary in the case described due to anti-racking braces within the frame.

ringi

Is there a way to use icynene on a “house wrap” enclosed wall that does not have sheathing boards?

I think the two main problems would be the speed that the foam comes out of the gun combined with the temperature of the foam as it expands. IMO although Housewrap is tough it isn't designed to cope with high pressure hot foam.

I didn't use a VCL. After getting the quote Icynene did an analysis for my construction which the BCO was happy with.