HUDDERSFIELD, England—There's another revolt brewing in the English heartlands.

"Let's boycott the shops that won't take cash—where are they?" Debbie Hicks yelled into a microphone in the town square on a recent Saturday. A few in the 200-strong crowd murmured some names—a coffee shop, a bakery.

"OK, we can do this," Hicks said. "It's not too late!"

Some 200 years after textile workers smashed newfangled looms here during the first stirrings of the industrial revolution, other rebels are worried about a newer technology: tap-and-go bank cards and smartphone payment apps.

Actual cash changes hands in only around 15% of transactions in the U.K., pushed out by the speed and convenience of using a card or phone. In parts of London, cash has become something akin to a prison currency like ramen noodles or cigarettes, circulated among panhandlers or those on the margins of society.

An unlikely coalition warns that by giving up cash, people could be losing more than they bargained for.