Render over Expermet (metal mesh) attached to Knauf cement panel,
celotex on inside.

I think it is Knauf cement panel, there are many, they come in planks
for cladding to sheets. The only note is they are very heavy,
something like 1.2 tons per metre-cubed. I think insulation-direct or
somewhere similar has several of them, they range from about £25 per
sheet up to something ridiculous if you go for very fancy advanced
materials.

I recall there are 2 figures for BR, #1 is the overall figure, #2 is
the minimum figure. You just need to meet the minimum figure with a
little extra elsewhere to compensate.

Any architect should be able to solve this one off the top of their
head. Glass is the other suggestion, and a floor to ceiling window is
quite attractive if that area inside can be used as a play area for
children to sit and watch the rain outside.