The Black Arrow has that skirt for the same reason that StarShip has a similar skirt. It is a (non-dropped) interstage.
Black arrow was intended to be orbit-capable by itself, but was also envisaged as being boosted by the Blue Streak first stage, in effect becoming the second stage of a different orbital rocket of greater capability, called the Black Prince.
from the articles listed below:
Blue Streak would have become the first stage of a projected all British satellite launcher known as "Black Prince": the second stage was derived from the Black Knight test vehicle,
As neither the Black Arrow nor the Blue Streak went very far into development, we never got to see this combination, but there is some discussion of its development at
http://everything.explained.today/Black_Arrow/
and
http://everything.explained.today/Blue_Streak_(missile)/
and
http://everything.explained.today/Black_Prince_(rocket)/