Luxury goods companies pride themselves on offering top-quality, exclusive products in sumptuous surroundings. But well-heeled consumers can now save themselves a trip to Bond Street or Fifth Avenue by choosing to buy a “vintage” Patek Philippe wristwatch or a “pre-owned” Hermes Birkin bag with a simple click of the mouse.

The idea of a secondary market for luxury fashion and accessories is largely anathema to an industry built on the strength of its carefully cultivated brands. Yet as online demand for used luxury goods grows, big brands are divided on how to respond.