LONDON—As the fashion elite filed into St. Paul's Cathedral on Monday to memorialize British designer Lee Alexander McQueen, the company he left behind is on the brink of making its first crucial trip down the women's catwalk without him.

The late Mr. McQueen, who built his label into one of the world's most daring fashion names, committed suicide last February. Four months ago longtime deputy Sarah Burton took over as creative chief of the London-based Alexander McQueen label, a small but symbolic part of PPR SA's Gucci...