The future of London is taking shape in the studio of Asif Khan. The architect is hard at work on an imaginative new Museum of London building that will combine the city’s history with its contemporary creativity. At 39, he’s one of the youngest architects to design such a major cultural institution in recent memory. It’s a “dream project” for Khan, who has spent the last 10 years building his reputation with temporary architecture like walk-through pavilions and tech-heavy installations.

Along the way, the born-and-bred South Londoner and father of two has picked up awards as varied as a Cannes Lions from the advertising industry and an MBE from the British royal family. A recent structure at the Winter Olympics was coated in the world’s blackest black, to dizzying effect. ...