Audrey and Sarah Thompson are poring over a notebook during a break from browsing stands at the Health Tourism Expo in Westminster. Sarah is in the market for some cosmetic dental work. Her mother is investigating weight-loss procedures. After speaking to a few providers—including some they know from Instagram—the Londoners are building a checklist. Does the company seem professional? Are the salespeople too pushy? They add one more: do the clinics, which are in Turkey, provide a translator?