I think the work on decompression was done by his father? His father did experiment on both himself and his son.
His uncle was the Liberal Party politician Richard Haldane who was the secretary of war for UK just before WWI and carried out some reforms which were pretty important in setting how the British army fought in the early part of the great war.
Haldane did amazing work on decompression and other things, using himself as a test subject in quite dangerous experiments.
His family was interesting, quite apart from himself. His sister Naomi is a well known Scots Author under her married Name Naomi Mitchison.