As high-end shoppers become increasingly mobile and connected, luxury retailers are testing new technologies that promise a more seamless experience between the physical and online worlds.

At a “Store of the Future” event at London’s Design Museum, the luxury e-commerce platform Farfetch showed off connected clothing racks, touch-screen-enhanced mirrors and sign-in stations that could help put data collected from customers online to use in stores, as well as harvesting material gathered during store visits to ease later orders on the web.

“How do you capture all of that fantastic information you gather in stores where customers touch and feel products?” asked Gavin Williams, head of product development at Farfetch.

Farfetch showed a scanner for customers to “log in” with their smartphones when they enter a store, allowing sales assistants to view customers’ profiles,…