There were probably several ways to forms threes from two ranks for the infantry. The Torrens manual (published shortly after the wars to replace Dundas) is an excellent window into the how the infnatry improvised on Dundas during the period. Torrens makes two ranks the standard. Because the Peninsular roads were such narrow tracks, marching three abreast was the standard.
Courtesy of Google, Torrens is now available at: http://books.google.com/books?id=wu4HO1l9Vg0C. See the bottom of page 42, where the commands THREES RIGHT and THREES LEFT are explained.
Why not just file march? Simple. The men were fallen in at shoulder dressing, 22" per Dundas, squeezed to 21" in Torrens. Consider the depth of a typical man's chest then add tunic, belts, backpack and mabe a kettle or shovel. File marching was almost impossible without the formation stretching out. It was a tactical objective that no march column should ever be longer than the unit when faced into line. In this way a column of several units could halt and form to a flank in seconds, ready to fight. This method as explained in Torrens gave a little more breathing room than file marching.
I expect that there were other ways of forming a march column by threes used during the wars, but this was the method agreed for the Torrens manual.
If you want a hard copy, it was rerinted by Naval and Military Press a few years ago and you can find plenty of copies for sale at a fair price, for example: http://www.alibris.com/search/books/isbn/9781843424529