Green sent a letter on Thursday, calling Field’s allegations during a radio interview last week “disgraceful.”
They will be replaced by David Hägglund who has been named sole creative director of both brands.
The appointment comes as Sir Philip Green shakes up the management ranks at Arcadia and its parent Taveta.
Yet to be sold is the Elizabeth Kennedy gown Dunham wore to the 2017 Met Gala.
Taveta is the parent of Green’s Arcadia retail group, which comprises fashion brands Topshop and Topman.
Brands are expected to migrate from the U.K. and France to the U.S.
Kelsie Hayes is one year into her business, and already becoming the go-to for the likes of Barneys New York, Eva Chen and Baja East.