Images like this were designed to further humiliate French military history
and elevate the status of Britain's vaunted armed forces. Here is a fairly factual accounting of the retreat:
During their meeting at La Belle Alliance on 18 June 1815, Wellington and Blücher decided that the Prussian cavalry would pursue the French. The Prussian chief of staff, Gneisenau, would take command of this pursuit. The exhausted allied troops would remain on the battlefield for the night. The Prussian II Corps under General Pirch would march in the direction of Mansart around midnight to cut of Grouchy's line of retreat. General Bülow received orders to march on Genappe.
After taking refuge in the last square of the Guard for some time, Napoleon and some of his officers fled to Genappes where he found his coach. He was almost captured by the Prussians when his coach got stuck in the mass of fleeing French soldiers. The Prussian Major von Keller managed to "capture" Napoleon's hat, coat and sword but the Emperor escaped.
The Prussian cavalry pursuit lost more and more of its momentum as the night progressed and eventually Gneisenau halted just south of Frasnes. The Prussians had captured about 8,000 French.
On the morning of 19 June Marshal Grouchy was still unaware of Napoleon's defeat at Waterloo. At about 1030 Grouchy received word of the Emperor's defeat. After some confusing moments General Vandamme proposed to march on Brussels to free the prisoners, cut of the enemy's line of communication and then regain France via Valenciennes. Soult's messenger, however, had brought orders for Grouchy to retreat to the river Sambre. Grouchy decided to do so by way of Namur, Dinant and Givet. In order to do so the Namur bridges had to be captured as fast as possible.
At 1130 Grouchy ordered General Exelmans to advance with his cavalry to Namur to take the bridges over the Sambre. The rest of Grouchy's command would follow at once, covered by a rear guard composed of Pajol's cavalry and Teste's infantry division.
This retreat was unhindered by General Thielmann's Prussians, many of whom had been routed after Grouchy's victory at Wavre. But General Pirch II Corps was on it's way to cut of Grouchy's line of retreat. He arrived at Mellery at about 1100 on 19 June but his troops were so exhausted that he had to let them rest. He spent the rest of the day there.
Two regiments of French Dragoons captured the Namur bridges at about 1600. At about 1900 the rest of Exelmans' cavalry passed through the city of Namur while Grouchy and IV Corps (General Gérard) were only about 10 km behind. Vandamme's III Corps reached Gembloux around 2100.
On 20 June Pirch's Prussians overtook the French and began to appear everywhere but where repulsed. Pirch then attacked again while the French withdrew through Namur but Teste's rear guard was able to hold off the Prussians at the cost of 1,500 Prussian casualties. Blücher then recalled Pirch and Thielmann and the Prussian pursuit of Grouchy's right wing ended.
Late on 21 June 1815, Grouchy's undefeated troops entered Phillipeville. He had managed to escape destruction or capture with about 28,000 men, most of his wounded, all his artillery and most of his equipment.
The telling remark comes when the "defeat" of Napoleon is handed directly to Wellington. And, while it is true that his leadership was critical, the war was actually won in the ensuing actions detailed above. Most of that legwork was done by the Prussians, not the English.