If you’re running a business, you might as well shut up shop for Christmas now. More than half your employees might be there, but they’re not putting their heart into it.

“Christmas seems to be starting earlier every year,” said Dan Rogers, co-founder of Peakon, a Danish startup that collects and measures data on employees.

A survey by the company found that 54 percent of British workers mentally check out for the holidays by Dec. 16.

At the younger end of the workforce, the great Christmas check-out comes sooner. Already Friday, six in 10 millennial workers have switched off, compa...