The first major victory for the New Model Army was the Battle of Naseby on Joune 14, 1645. The numbers of both forces vary according to sources, but my own sources conclude that Parliament had 13,000 men, about 7,000 infantry, 5,500 cavalry, and about 1000 dragoons. The royalist army consisted of 8000 men, about 50% infantry and 50% cavalry (Ross, 11).

If you follow with me on the map above (Parliament/New Model Army in blue, Royalist/Cavaliers in red), you can see that both armies have their infantry in the center, with cavalry on both sides. Parliament also has a hidden regiment of dragoons off to the left hand side of the field lead by Okey. Prince Rupert lead his Royalist cavalry in a charge against Ireton's cavalry after Okey's Parliamentary dragoons opened fire into Rupert's ranks. This charge swiftly went right through Ireton's cavalry, but kept going! The undisciplined forces under Rupert went in search of plunder or a baggage train, instead of continuing the battle. Now a third of the Royalist cavalry gone, the Infantries advanced to engage each other. At first the outnumbered royal infantry held their own lines strong, But Cromwell, commanding the parliaments right cavalry, charged against Langdale's cavalry and continued not to the baggage train, but into the royal infantry right flank, then the dragoons and Ireton joined on the opposite flank for a charge. Parliament's new model army won handsomely and the battle ended quickly. (Ross, 11-12)

Ross, W. G. “The Battle of Naseby.” The English Historical Review, vol. 3, no. 12, 1888, pp. 668–679. JSTOR, www.jstor.org/stable/546960.

Image thanks to “Home.” British Battles, www.britishbattles.com/english-civil-war/battle-of-naseby/.