(Kind of relying on memory here since I'm five hundred miles away from my books. Any sources I list may therefore be a little unreliable)

By the Revolutionary War, I assume you mean the American Revolutionary War? In that case, the column was not actually a common formation for the British in that war: the British infantry's preferred formation from the American Revolution, through the French Revolutionary War, all the way to the end of the Napoleonic Wars, was the extended line, a formation three, and later two, ranks deep that could bring the maximum number of muskets to bear. Despite the stereotype, the British Army had in fact adapted a great deal to fighting in North America, making use of dispersed line formations with far greater separation between troops and light infantry companies as early as the Battle of the Plains of Abraham in 1759 during the Seven Years' War.

Moving on to the column formation, the idea of attacking in column was one of a series of military reforms developed in France after its humiliating defeats in the Seven Years' War of 1754-1763. It was considered that a narrow, deep formation like a column of troops would be much easier to control across the broken ground of the battlefield than a long line, and so much faster to get into action. The disadvantage to the column was that it was far more vulnerable to artillery, as roundshot smashing through it would knock down multiple ranks of troops, whereas a cannonball hitting a line would knock down three men at most. Therefore, it was considered dangerous to launch column attacks without artillery superiority, though since Napoleon was a gunner by training and prized artillery accordingly, this was not a particularly great problem for the French as the Napoleonic Wars went on.

It's common to see, particularly in British histories, the idea that the column was a shock formation designed to smash through thin lines with sheer weight of numbers at the point of a bayonet. While this may indeed have happened early in the French Revolutionary Wars with poorly-trained levies, the column was in fact designed so that a battalion could rapidly cross open ground then quickly swing into line and begin an exchange of musketry with the enemy. At the Battle of Austerlitz in 1805, several French battalions dispersed from columns into skirmish order at the run and began a musketry exchange with the Russians and Austrians until columns in the second line came up to deliver the final blow. A common French brigade formation was ordre mixte - "mixed order" - which often took the form of a battalion in the centre moving into line while keeping a battalion in column on each flank to provide defence against cavalry or to overcome the enemy's flanks.

The column's disadvantage lay in fighting in hilly country, which accounts for much of the British Army's repeated success against the French in the Peninsular War: the genius of Wellington's "reverse slope defence" was to position his battalions in line behind the crest of a hill, which meant that the French columns would not just have to face an exhausting climb to reach them, but also had no idea when to begin the move into line. Consequently, the British were repeatedly able to catch the French by surprise as they crested the hill or as they attempted to move into line early and were disordered.

As for when it began to fall out of use, the Crimean War of 1853-1856 spelled its doom when British and French troops, despite fighting on a tiny beachhead with incompetent commanders and staffs, were repeatedly able to fight off Russian column attacks using new rifled muskets, which were vastly more accurate than their Napoleonic Wars predecessors. That same grim scenario was repeated time and again during the American Civil War when both Union and Confederate troops tried to storm entrenched defences guarded by men with rifled muskets. The Austrians clung gamely on to the formation as late as the Austro-Prussian War of 1866, but at that point the winds of change were truly blowing against them: Prussian troops equipped with accurate breech-loading rifles moved in loose skirmish lines that were able to outflank Austrian columns and completely devastated them with rapid individual fire. You will hear some stories of troops attacking in column from the First World War, especially from 1914, but more often than not those were marching columns, not battlefield formations, that were caught by surprise, for example the German Army running into the unexpected British defences at the Battle of Mons.

Sources:

Mark Urban, Generals: Ten British Commanders Who Shaped the World

Paddy Griffith, French Napoleonic Infantry Tactics 1792-1815

Philip J Haythornthwaite, British Napoleonic Infantry Tactics 1792-1815

Peter Snow, To War with Wellington

Geoffrey Wawro, The Austro-Prussian War: Austria's War with Prussia and Italy in 1866