From his position in the Captain, near the rear of the British line, Nelson had a good view of events as they unfolded. He saw as, at 1pm, the Culloden began to open fire upon the rear-most Spanish ships, with the Blenheim approaching behind. He had seen Jervis' signals, and he saw that the Britannia was not turning.
Alarmingly, he then noticed that Córdova's division was beginning to turn to the east with the intention of getting round the rear-most British ships. He knew that if he continued to follow the Britannia and ignore Jervis' order to turn, the Spanish would be given time to get past them and become a serious threat.
So Nelson, in a remarkable display of initiative and ingenuity, took it upon himself to join the British van. He wore out of the line - that is, he turned away from the wind (tacking involved turning into it), and away from the Spanish. This was a faster way of turning, as it meant that the wind could catch the sails as the ship turned away from it. He then cut back through the line, ahead of Captain Collingwood's Excellent, and sped towards the Spanish and Troubridge's Culloden. Thanks to his quick-thinking and seamanship, he reached them just 10 minutes after the Culloden engaged.
It was a risky move, because as the Captain approached alone she would come under heavy fire from five big Spanish ships, which was potentially devastating. But the Spanish gunnery was not very fast or accurate, which Nelson had probably counted on after his earlier visit to Cadiz and assessment of the Spanish ships and seamen.
In contrast, the Captain's gunners were highly trained, disciplined and experienced, and subjected Córdova's ships to fast, heavy and accurate fire. The move and devastating attacks took Córdova by surprise, and he gave up on his attempt to turn and continued on his original course. Later, Captain Miller of the Captain described the manoeuvre as like "turning them as two shepherd's dogs wou'd a flock of sheep".
"Engage the Enemy More Closely"
10 minutes after Nelson's move, Jervis signalled for the whole of the rear division to join him. Abandoning the strategy of all turning at the same point, they rushed to get into the action where they could. The Barfleur was a fast sailer, and Waldegrave had her wear in the same way as Nelson's Captain had done, and was able to join the line directly behind the Victory. The Britannia and Namur were slower and reached the end of the line, and thus hardly took part in the battle at all. The 64-gun Diadem was very quick, and joined the end of Parker's van division, behind the Irresistable. Collingwood's Excellent, also a fast sailer under his seamanship, was able to get ahead of the Victory.
Now he had a number of ships supporting the Culloden and Captain, Jervis signalled the fleet to 'engage the enemy more closely' - in other words, engage in a brutal, short-range melee attack. This would later become Nelson's favourite signal, well-suited to his fierce and ruthless desire for short and decisive battles. However, the speedy Diadem and Irresistible got a little carried away and Jervis later had to order them to cease firing as they came too close to the Victory and Excellent.
By this time, the Spanish were completely confused and disorganised and in no semblance of a line. As the British van reached his fleet, Córdova signalled 'Each unit should enter combat as soon as it can'. But because of the erratic positioning of the ships, some of the ones in the front didn't see the signal.
Later, Córdova said that the way the British fought, "in great good order, with a heavy and well-directed fire, decided the action in their favour."