I don't know the British regulations, but per analogy to the French and Prussian ones, I presume that wheeling by threes in the infantry is different from the manoeuver in the cavalry.
In order to form a marching column in the infantry, usually, the line of a peloton would be split up in smaller sub-units (two sections in the French army, several Sektionen in the Prussian army). These sub-units would wheel (forward in most of the cases) by 90 degrees to the right or left as an entity, as they are, in two or three ranks, taking the flank man in the front rank as pivot for the movement.
I wheeling by threes is ordered, the sub-unit would consist of three files (= frontage of three men) only. The British infantry being formed up in two ranks, your 90 men in two ranks would have a frontage of 45 men when in line. Wheeling to the right by threes, the resulting column would have of a frontage of 3 men, and consist of 15 sub-units, each of 6 men in two ranks, each of these sub-units being seperated from the next by a free space of the width of one man.
However, a man knowledgable in the British regulations would have to confirm this.