Nobby_66
Vital Football Hero
I believe local councils have that power and have had for some weeks. Our local Councillor threatened to lock down Southend when the beaches were getting overcrowded a few weeks ago.I think a local mayor would have the power to impose a local lockdown if he thinks it's needed. He would of course then have to take the flak from those who disagree with it.
However, as you say, they would be left with lots of unhappy businesses that rely on summer trade to get them through the rest of the year.