I think your being a bit harsh on Mr Burl. The theories about the axe trade are the 'best fit' we have based on solid evidence and field work.
You ask for evidence - hit the books fella, it's all there.
I'll scratch the surface for you.
Scandanavian, Alpine, and Breton axes are found around Britain. Large concentrations of axes from the Lizard (group I) found in Suffolk, the greatest concentration of Langdale axes (group VI) occur most commonly in Lincolnshire and the East Midlands, Group VII axes from North Wales are found in Kent, to name just three examples. I dunno about huge axe markets but there is plenty of evidence of the passing of good amounts of axes between communities, which implies trade.
People were travelling the length and bredth of Britain and Ireland seeking axes, these were people who had access to local stone that would have done the job just as well but they chose to undertake journeys to aquire 'exotic' axes for some reason. Many of the finest axes had no practical use whatsoever and have been found deposted in burial monuments, henges and other ritual settings.
No lay-line-ologies there just years of solid fieldwork & research.