Playford 1710; Bernard Bentley 1962.

Video: https://upadouble.info/dance.php?id=BlackwellHall

A1 M1 between W2 and W3 to between C3 while
   W1 between M2 and M3 to between C2,
   C2 move up.
   Set to each other (TWICE?)
A2 C1 both cast R to 2nd place
   Cross R shoulder and turn L around W2 or M3 so M1 between C2, W1 between C3
   Set to each other.
B1 Cast over L shoulder and move to middle position proper and 
   hey on own side (R Shoulder from middle position, which is finishing point)
B2 4 changes of R&L (top 2 couples)

   
A1 M1 between W2 and W3 to between C3 while
   W1 between M2 and M3 to between C2,
   Set to each other (TWICE?)
A2 C1 both cast R to 2nd place (C2 make room)
   Cross R shoulder and turn L around W2 or M3 so M1 
   between C2, W1 between C3. Set to each other.
B1 Cast over L shoulder and hey on own side (R Shoulder
   from middle position, which is finishing point)
B2 C1 and C3, 3 changes of R&L (bottom 2 couples)

Video: https://upadouble.info/dance.php?id=BlackwellHall-3Couple

My own attempt at a danceable choreography (2026-10-23) us a triple minor proper as follows:

A1 M1 between W2 and W3 to between C3 while
   W1 between M2 and M3 to between C2,
   Set to each other TWICE
A2 C1 both cast R to 2nd place (C2 make room)
   Cross and turn L so M1 between C2, W1 between C3
   Set  TWICE
B1 Cast over L shoulder and hey on own side (R Shoulder
   from middle position, which is finishing point)
B2 4 changes of R&L (top 2 couples)

If danced as 3C set, actives move to bottom at end of R&L and C3 move up. Suggest actives go down middle and C3 up outside in case C1 is starting next round.

https://exploring-london.com/2015/03/27/lost-london-blackwell-hall/ says

 A trade hall for the wool and cloth trade, Blackwell Hall, also known as 
 Bakewell Hall, once stood on the east side of Guildhall Yard in Basinghall 
 Street.