Plenty would happily work "a bit" or "in some way", but there's not a lot in the system to support assisted/flexible/partial working etc.
If you have injuries, ailments, illnesses, they're still asking you to work 40 hours or go fully on sick, rather than supporting a "however many hours you can manage" and a small topup to maintain a basic standard of living.
These used to be part of the system, in the earlier part of the "working tax credits" era.