The pair are believed to have rented a five-bedroom house together in Wimbledon, close to the former family home.
Robertson attended £29,600-a-year Canford School, in Wimborne, Dorset, where he got two Ds and an F in his A-levels. In 1996, he and friend Quentin Griffiths set up Entertainment Marketing.
Four years later they launched Asos with £2.4m, mostly borrowed from friends and family, and turned it into an online giant - making him one of the richest men in Britain. Robertson stepped down from the role of chief executive in 2015, making way for current boss Nick Beighton, but has remained a non-executive director.