Several weeks ago I posted a photograph of myself in an Anglo-Catholic social media group, vested for the procession into the sanctuary in alb and chasuble and...a Canterbury cap. The majority of the people who responded to the photo were approving (thumbs, hearts, etc), while two or three expressed disapproval (a laughing face or an angry face).
One commenter, a deacon in my own Anglican jurisdiction, stated that the Canterbury cap was "Genevan" and "too protestant," and if I were to don any head covering while wearing the chasuble it should be the biretta. I responded with a jibe from Percy Dearmer, that to exchange the Canterbury cap for the biretta would be like an English soldier preferring the German helmet with the spike on top.
Of course, the more substantive argument to be made is that the Canterbury cap predates the biretta. Indeed, it is the progenitor of both the biretta and the academic mortar board (which, if you look at paintings of Anglican clergy in procession at coronations, was also worn by Anglican priests and bishops with surplices and copes. Don't worry--I'm not arguing for a return of the mortar board in Anglican services). If the biretta can be donned with the fiddleback chasuble, why shouldn't its predecessor be donned with the gothic chasuble (and at the same times during the service, rather than just at "choir services")?
The deacon who chided me for wearing the Canterbury cap instead of the biretta commented that the Canterbury cap was "anachronistic, as is your churchmanship." Very true. I am intentionally being anachronistic in my desire to reach behind the divisions of western Christendom to celebrate Christianity in a way that is Catholic yet intentionally English. I celebrate the Eucharist with an English liturgy, with Sarum ceremonial, and in gothic vestments. I know I don't need to wear a hat, but if I do, I think it should signify the same English Catholicity.