The UK's National Health Service (NHS) is definitely up there.

There are 1.6m people working for NHS and about 41m people of working age in the UK. So that's about 1 in 26 (or 3.9%).

Sources: https://www.kingsfund.org.uk/projects/nhs-in-a-nutshell/nhs-..., https://fred.stlouisfed.org/series/LFWA64TTGBQ647S