Britain was, up to that point, never a land power and its armies had very limited involvement with the likes of the 30 Years' War that would have exposed them to current tactics and formations; her strength lay mainly in the navy and diplomacy. Take their famous victories in the Hundred Years' War for instance. At Crecy, the French cavalry ran up a hill onto longbow men with the Genoese crossbowmen largely out of commission due to the rain soaking their weapons prior and their pavises being left behind. At Poltiers, John II had his French knights dismount to keep the horses from rolling up the lines in retreat as in Crecy and got captured as his men became fodder. At Agincourt, the French let the British march up and pitch defensive constructs only to charge at them over a muddy field. During the days of the Great Armada, the Duke of Parma estimated that 30K-50K Spanish troops could take the entire British Isle and Queen Elizabeth did, in fact, pour all of her treasury, as did her father, into shipyards. The Spanish lost all heart when 16K of their army died from disease and bad drinking water, thanks to Drake's raid on Cadiz that had disrupted the supply of properly dried wood for water barrels.

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Now, let's look at what Cromwell was dealing with during the Civil War. At the Battle of Edgehill, the Royalists held the initial advantage when Fortescue and Ramsay fled while Rupert and Byron's cavalry overran the guns and infantry. On the other flank, Wilmot's Royalist had routed Feilding's units but his scattered when the soldiers were going after plunder instead of charging at the Parliamentarian rear. This gave the Parliamentarian horse enough time to overrun Ruthven's center. The battle ended in a draw as did many others in this war.

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When Cromwell's Ironsides arrived late to the field, he observed thus:

Your troopers are most of them old decayed servingmen and tapsters; and their troopers are gentlemen's sons, younger sons and persons of quality; do you think that the spirits of such base and mean fellows will ever be able to encounter gentlemen that have honour and courage and resolution in them?

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Then Cromwell got a chance to shine at the Battle of Marston Moor. Rupert had marched his army, despite being outnumbered, towards the siege of York and had stopped for the rain. Leven of the Parliamentarian side decided to surprise the unprepared Royalists who were breaking to sup. Byron's Royalists charged at the Parliamentarians disregarding an order to take a defensive position and Napier's gunners were unable to fire lest they hit their own cavalry. Across the battlefield, Goring's cavalry had better luck with the counter-charge but the unit broke for loot. The disciplined Ironsides made short work of Byron and Goring's cavalry.

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Cromwell performed simple maneuvers that required less "military prowess" and more discipline. Larger strategy and tactics were derived from the likes of Leven and his contributions were mostly driving into his troops faith and making sure his men were led by those of meritocracy over nobility/political status. It did also help that his side outnumbered the other.

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A similar case can be found in the East. While the brilliant Admiral Togo of the Russo-Japanese War, aka Nelson of the East, spoke of Admiral Yi of Joseon, he said the following:

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It may be proper to compare me with Nelson, but not with Korea’s Yi Sun-sin, for he has no equal.

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However, Admiral Yi actually had no naval experience as he was an officer of the army fighting nomads up north. He focused on gathering civilian intelligence and getting the numbers advantage in cleanly executed enveloping maneuvers. He lost no battles and fought 13 ships to 133 after being tortured by his king but he can't be put on the same level as the aforementioned sailors, especially on the open sea.