Tough times for Sir Mick Jagger's family ... a desperate search is underway for his granddaughter Assisi Jackson’s longtime partner, who’s vanished in Cornwall, UK.

Alexander Key, a 37-year-old chef, was last seen Friday afternoon at the Cobweb Inn in the village of Boscastle around 2:30 PM ... CCTV shows him leaving about an hour later, and by Saturday night he was reported missing to Devon and Cornwall Police, The Telegraph reports.

Assisi’s mother, jewelry designer Jade Jagger -- Mick and Bianca’s daughter -- shared photos of Alexander in a plea for help, showing him in a bright orange jacket with peroxide blond hair.

Alexander -- who shares two young daughters with Assisi, is described as medium build -- and cops say they’re increasingly concerned for his welfare as the search widens across the area.

Anyone with any information is urged to contact police immediately.