I am converting an old cow shed for residential use and must install a radon barrier with sump and outlet. It makes sense for ease of groundwork to run this outlet alongside (one of) the air inlets for a wood burner. Hence they will appear on the outer wall of the building next to each other, except insofar as I deliberately create a gap between them. Aesthetically it would be good to have at least a small (200mm, say, centre to centre) gap between them, but are there any building regulations which cover this question?

In any case, I think it very unlikely that any radon which is drawn up the air intake poses any risk to health as it will be emitted from the building in due course (for a second time!) through the chimney.

https://www.ukradon.org/cms/assets/gfx/content/resource_2722cs33267e5dc5.pdf

There's nothing definitive about building regs that I can see. There are statements like away from doors, windows and ventilation grilles, but no indication of distances or legal requirements. The general thrust seems to be to design the system so that there's no risk even if the duct has leaks, so making your stove pipework effectively part of this circuit sounds like a bad idea. It may be better to construct a separate channel for the radon duct, even if that means slightly more groundworks.