The late 1700s/Early 1800s because of several factors. In Britain when Wig powder was taxed in 1795 by the Duty on Hair Powder Act 1795, costing one guinea a year, a large expense at the time. The other factor was that King George IV who was very influential on British style and fashion of the day stopped wearing one and went bareheaded instead.

In France wigs were abandoned following the French revolution as a symbol of the aristocracy.

With wigs out of style in the two most powerful and influential countries at the time, the rest of the world soon followed.