I don't think you'd need to go to the absurd detail that American healthcare does.
Some variation on the "NHS Injury Cost Recovery scheme" would seem to be appropriate.
This little known provision allows the NHS to reclaim the costs of treatment from a third party causing the injury.
If the definition of 'injury caused' could be widened to include something like 'inability to complete treatment' then it's covered.
The easiest to read explanation I've found is at https://www.majortraumagroup.co.uk/news/making-claim-help-nhs-injury-costs-recovery-scheme/