One group working on this is the Natural Material Innovation group at Cambridge: https://www.natmat.group.cam.ac.uk/research/natmat
"Timber Towers" London proposal: https://www.natmat.group.cam.ac.uk/news/timber-towers-could-... (2019)
(encountered via the easy-listening of BBC Radio 4's 39 Ways to Save the Planet: https://www.bbc.co.uk/programmes/m000qy43 )