The rebranded event, known until recently as the British Fashion Awards, was held on Monday at Royal Albert Hall.
Analysts brushed off consequences of Renzi's resignation on luxury.
The tailor is seeking $1.9 million in damages, according to his attorney.
Constance Jablonski, Coco Rocha and Olivier Theyskens turned out.
The Beverly Hills-based fine jeweler inaugurated it last week with a party featuring performances by The Four Tenors, David Foster and Babyface.