I am not sure about "peculiar" British arrangement. A French square formed from a column of divisions at peleton distance (the French most common tactical structure) formed in exactly the same way, except that its sections did not double up so there were only 3 ranks in each face. Also any nationality "solid" square formed from a close column had exactly this same layout.

One feature is that the 4 files on the extreme ends of the sides of the square are in fact men from the 2 front and 2 rear companies, so fire hitting the square in the flank could hit men from any company, although there will be twice as many potentially vulnerable ones from the intermediate companies than from the front and rear ones.

Rod