I'm sceptical about some of the claims about the long-term productivity impact of four-day weeks. I suspect in the short-term it works because of the combination of diminishing marginal returns (for every extra day you work, the marginal benefit of the extra day decreases) plus people putting in extra time on the remaining four days; so over a longer horizon, if working patterns adjust back to normal after the novelty wears off (i.e. people stop putting in the extra hours and go home at normal time), then I think four days should lead to less work getting done than five days (albeit still more than 4/5ths of the work due to the diminishing returns).

But long-term experiments are good for testing out hypotheses like this. Also for central government to dictate to local government what they can and can't do is fucked up - the voters of South Cambridgeshire have elected a Lib Dem council (reelected barely a year ago winning 35 of the 45 seats available) and it's up to the voters of South Cambridgeshire to decide whether experiments like this represent value for money, not some angry Brexiter at Westminster.