Shares of Stitch Fix fell after hours on Monday after the online styling service said it expects falling sales through the months ahead and plans to exit its business in the U.K., as a still-cautious customer pulls back on wardrobe experimentation.

Management, during Stitch Fix’s SFIX earnings call, said its clients were “still being cautious” in an economy where shoppers are still finding their footing after dealing with big price increases since last year.

“Our...