Hayley Paige spent the majority of her life tumbling around in sparkly leotards as a competitive gymnast. In her spare time, she learned how to sketch and sew, and started making herself dresses.

There’s a certain alchemy to fashion design, a magic in the way a two-dimensional sketch becomes a pouf of teal brocade on the runway. At Erdem Moralioglu’s studio in the eastern reaches of London, ...