Phair, chief strategy officer at Farfetch, replaces Natalie Massenet who was head of the organization for five years.
The new fund was formed with Nick Brown and is also backed by Matchesfashion.com cofounders Tom and Ruth Chapman.
The BFC hosted a surprise party for its outgoing chairman.
The designer will be the first recipient of the Special Recognition Award for Innovation.
Two fashion industry events took place on consecutive nights: one that had to do with Graduate Fashion Week and the other with a new antibullying campaign.
Angela Ahrendts, Daniel Zhang, Natalie Massenet and Nas will join Bernard Arnault on the jury of the inaugural LVMH Innovation Prize.
Speakers will include Will.i.am and William Shu, founder of Deliveroo.
It’s rumored that Farfetch, as well as Daily Harvest and Dirty Lemon, are among the first companies Massenet and Brown will invest in.
Massenet will look for ways to reach the demanding, international, consumer.
Massenet announced the news via an Instagram post
The Mail on Sunday speculated that she could be joining Farfetch.com.
The BFC made the largest single donation to its Education Foundation following the Fashion Awards 2016.
The night before the British Fashion Awards, designers came together at the Moda Operandi HQ for Champagne and cocktails.