At the beginning of the battle, Lieutenant-Colonel James Webster commanded the left half of the British line (the 23rd and 33rd regiments, aided by part of the British Guards and a company of jaegers). With these men, he overcome part of the North Carolinians defending the rail fence (Part 4), and got into a nasty fight with William Washington’s flank corps in the woods (Part 5). During these actions, Webster gravitated to wherever the action was hottest. He boldly led the 23rd Foot through the open fields in front of the North Carolinians on the first line, and then joined the 33rd Foot after its flank was threatened by Washington. 
Webster’s men fought with skill and courage, and eventually they pushed through the woods to the Americans’ third and final line. Probably their advance was facilitated by the early and almost total collapse of the second line troops nearest them (i.e., Randolph’s and Holcombe’s regiments of Lawson’s brigade, see Part 6).
In any case, Webster reached the third line before the rest of the British army. Many of the Continentals on the third line were placed on a wooded hillside and hidden from view; Webster, however, could see that part of the line which abutted an old field to his front. He ordered an attack.
According to Lieutenant-Colonel Henry Lee:
Webster… sought with zeal the continental line; and presently approached its right wing. Here was posted the first regiment of Maryland… The enemy rushed into close fire; but so firmly was he received by this body of veterans, supported by Hawe's regiment of Virginia [i.e., the 2nd Virginia] and Kirkwood's company of Delawares… that with equal rapidity he was compelled to recoil from the shock. 
A soldier with the 2nd Virginia vividly recalled that the Continentals were positioned “along behind a fence near a creek”, and that “when the British marched up towards us we fired upon them and there was a dreadful slaughter indeed… he could have walked for one hundred yards upon dead men and not have touched the ground.” 
According to Lee, Webster fell back across “a ravine in his rear,” “occupied an advantageous height,” and waited “for the approach of the rest of the line.”
Then, the men in Washington’s flank corps tried to exploit this reverse. Sergeant-Major William Seymour of the Delaware regiment wrote, “Washington’s Light Infantry… pursued them up a very steep hill, almost inaccessible”. The British “lay concealed in ambush,” and when the Americans approached they “[rose] up, and [poured] in a very heavy fire” by which the Americans “suffered very much” and “were obliged to retreat”. 
Webster's men (at center) approach the 3rd line (here and below, click to enlarge). The blue-coated Continentals are, from left-to-right, the 1st Maryland Regiment, the 2nd Virginia Regiment, and the 1st Virginia Regiment (cf. the third line at Guilford Courthouse). Some of the Virginia militia can be seen retreating from the second third line or rallying behind the Continentals.
The 33rd Foot is staggered by a volley.
“Washington’s light infantry” pursue Webster's men.
William Seymour served in Captain Robert Kirkwood’s company of the 1st Delaware Regiment and kept a journal during the southern campaign of the Revolutionary War. At Cowpens, Kirkwood’s company participated in a sudden American counterattack that broke apart the British and turned the battle into a major American victory. Something similar appears to have been attempted on this occasion. The British had fought their way through the militia, only to be bloodily repulsed by the Continentals. The Americans then made a bold counterattack. However, the counterattack at Cowpens is famous, while this counterattack at Guilford Courthouse has been almost wholly forgotten (presumably because the former succeeded while the latter did not). At Cowpens, the American counterattack was made by all of the Continentals and across a short expanse of fairly level ground. At Guilford Courthouse, only “Washington’s Light Infantry” are credited with the counterattack, and the movement was made across a wider and more difficult expanse of ground.
Washington’s Continental light infantry included Kirkwood's Delaware light infantry company, and Captain Phillip Huffman's Virginia light infantry company [cf. Babits & Howard (2009) Long, obstinate, and bloody: The battle of Guilford Courthouse]. Possibly some or all of Colonel Charles Lynch’s Virginia riflemen, who also served in Washington’s flank corps, participated in this counterattack.
1. See the accounts by Charles Cornwallis, Charles Stedman, and Roger Lamb in this compendium of sources.
2. Henry Lee (1812). Memoirs of the War in the Southern Department of the United States.
4. William Seymour (1896). A journal of the southern expedition: 1780-1783. Papers of the Historical Society of Delaware, 15, 3-42.