There is a good sketchmap in the Waterloo Letters – P38
Unfortunately the map is folded in this source
link
I think this is the same map here
The memorandum in letter is interesting:-
Prior to the action "the Brigade had been standing in line in the hollow behind La Haye Sainte, with their right about 250 yards on the left of the Brussels road".
"The cannon shot that passed over the crest of the ridge was beginning to fall pretty fast, the Brigade was advanced slowly towards the ridge by the Troops wheeling to the left, and taking ground to the right by the flank march of Threes".
"On arriving very near the top of the ridge the Column fronted, and halted for perhaps four or five minutes.
The Marquis of Anglesey came up at speed….wheeled the Royals and Inniskillings into line and ordered them to charge, the Greys forming a second line in reserve".
Wyndham #40 – Greys. "We moved up, and I think took ground to the left to get more under cover of the hill."
"We afterwards wheeled into line".
Stratton relying on Maddox #43 – We were in column and wheeled into line.
Miller #46 even mentions the Inniskillings dismounting at the foot of the hill, marching up the hill on foot then remounting at the top of the hill".
In the unpublished letters Clarke #31 mentions the Greys being in line "then wheeled half squadrons to the right thus forming an open column to the right. Subsequently they received a sudden order to wheel again 'left into line'and attack immediately."
The interesting thing about these columns is that the Troops were not in a column one Troop behind the other facing the French but one Troop behind the other facing to the flank. This would allow lateral movement before wheeling the Troops into line.
The flank march by threes means that the Troops were first in line, then wheeled by Troop to form an open column facing to the left, then performed "Threes Right" to form a flank column each Troop now having a frontage of six horses. Each column then moves up in parallel to the line of deployment then "fronts" back into the open column of Troops. Flank march by "threes" is a normal means of adjusting the location of a line rather than advancing in line and dealing with the obstacles in the way.