Statements about the British forces at Hanging Rock were made by British and American participants and their contemporaries. Most reliable is Lieutenant-Colonel Francis Rawdon's statement that Hanging Rock was defended by "400 provincials and 800 militia" .
The Provincials included men from three different regiments: The British Legion infantry, The Prince of Wales’ American Regiment, and the Royal North Carolina Regiment . Total losses for the Provincials were 38 men killed, 69 wounded, 71 missing . The strength and losses of each unit are as follows:
Prince of Wales’ American Regiment: Lost 93 of 181 men (51%) 
Royal North Carolina Regiment: Lost 50 of approximately 100 men (~50%) 
British Legion Infantry: Lost 35 of 161 men (22%) 
In regards to the number of missing, 43 men were captured by the Americans . Half of these men were privates and noncommissioned officers of the Prince of Wales’ American Regiment that surrendered to the Americans during the fighting . The other half had been both wounded and captured (most, if not all of these, were also of the Prince of Wales’ American Regiment).
Two forces of Loyalist militia were at Hanging Rock: Colonel Samuel Bryan’s North Carolina Volunteers (called in some sources the North Carolina Refugees, because they had been forced to flee their native state), and Colonel Henry Rugeley’s South Carolina regiment . Bryan organized between 600-700 men in North Carolina, however, he brought only 250 men with him to Camden after Hanging Rock . Bryan surely had a fair number of his men killed, wounded, or missing as a result of the battle, but there is no reason to believe that his losses ran into the hundreds. Rather, his original force had likely been greatly reduced by August 6 by desertion, sickness, and combat .
Rugeley’s regiment, like other South Carolina Loyalist militia regiments, likely numbered around several dozen men .
Some sources claimed Bryan lost many men , while others thought his losses were negligible . One clue to Bryan's actual loss is Thomas Sumter's account of the battle, which implies that around 30 of the Loyalists were captured . As these men were likely wounded before being captured, and as a common ratio of killed to wounded during the war was 1:3, Bryan's losses were likely in the neighborhood of 40 men.
It is not possible to make any estimate of losses in Rugeley's regiment.
Based on this rather imperfect information, I estimate the total force of Loyalist militia at the battle of Hanging Rock as near 400 men. The numbers listed above suggest a lower total (250 for Bryan's survivors + ~40 for Bryan's losses + several dozen for Rugeley = ~325), but this does not include men that would have remained missing, or would have left Bryan's command altogether, after his defeat at Hanging Rock.
Division of Forces:
The British were divided into three camps. The center camp included the British Legion infantry and the Royal North Carolina Regiment . The right camp included Bryan's North Carolina Volunteers . The left camp included the Prince of Wales' American Regiment . It is not possible to place Rugeley's regiment at any one of these camps with confidence, but the center camp seems most probable .
1. Letter from Francis Rawdon to Colonel McMahon, January 19, 1801.
2. Todd Braisted (2001). A History of the Prince Of Wales' American Regiment; The Revolutionary War Sketches of William R. Davie [extract]. Davie's account also appears in, John H. Wheeler (1851). Historical Sketches of North Carolina from 1584 to 1851, Vol. 1.
Some secondary accounts claim that the King’s Rangers, commanded by Colonel Thomas Brown, were at the battle. This stems from a misreading of Tarleton’s description of the battle, which refers to Brown’s regiment, but means Colonel Montfort Browne, commander of the Prince of Wales’ American Regiment. Browne was not present on this occasion, and command of the Prince of Wales’ American Regiment was left to Major John Carden. Because of absences in the field officers for the other regiments, Carden also commanded the entire post.
3. Enclosure in a letter dated August 20, 1780 from Charles Cornwallis to George Germain. In K. G. Davies (Ed.), Documents of the American Revolution 1770-1783 (Colonial Office Series), Vol. XVI. Irish University Press.
4. Braisted, ibid., Donald E. Graves. Guide to Canadian Sources Related to Southern Revolutionary War National Parks. (Retrieved February 6, 2010).
5. See this return of losses; Braisted, ibid. The Royal North Carolina Regiment appears to have been a detachment only; its strength was estimated from subtracting the strength of the Legion infantry and the Prince of Wales’ American Regiment from Rawdon’s stated 400.
6. Braisted, ibid. The strength of the regiment is estimated by adding these losses to their strength on August 15, 1780. Approximately forty of the Legion infantry were in the companies of Patrick Stewart and Charles McDonald, according to Banastre Tarleton’s A History of the Campaigns of 1780 and 1781. These companies arrived at the close of the battle, and William Davie claimed they lost 1 man. Of the Legion infantry who were present at the beginning of the battle, 34 men were lost of approximately 121 (or 28%).
8. National Archives of Canada: List of the Killed Wounded & Prisoners of ye P.W.A.Regt [posted on a geocities website that is no longer available].
9. Braisted, ibid.
10. Judicary report on Samuel Bryant, John Hampton and Nicholas White, April 5, 1782.
11. Desertion, as noted previously, was a natural occurrence when militia units were not regularly employed. Sickness was likely a factor given that Bryan's men were encamped briefly at Cheraws, South Carolina, where the 71st Foot became debilitated. Losses in combat occurred primarily at Colson's Ferry, North Carolina, on July 21 (see letter from Thomas Blount to Abner Nash, July 23, 1780), and at Hanging Rock on July 30 (see Davie, ibid.).
12. By way of comparison, Mathew Floyd's Loyalist militia regiment, which fought at Hill's Ironworks, Williamson's Plantation, and (probably) Rocky Mount had only 30 men in mid June. See Michael C. Scoggins, More on the Battle of Hill's Ironworks, Volume 2, Number 7 of Southern Campaigns of the American Revolution. This unsourced website gives Rugeley's regiment 40 men at the battle.
13. For example, Davie, ibid., claimed that during the battle, Bryan's men were "routed with great slaughter."
14. Tarleton, ibid., stated that "Colonel Bryan's North-Carolina refugees were greatly dispersed, but did not suffer considerably by the fire of the enemy."
15. Letter from Thomas Sumter to Thomas Pinckney, August 9, 1780.
16. Davie, ibid.
17. The rationale behind this placement was described in this post.
18. The site of their encampment was determined by process of elimination in the absence of clear statements among the available sources.
19. Davie said Bryan's camp included "Bryan's Regiment, and other Loyalists." This can be interpreted to include Rugeley's regiment, but it is not a necessary conclusion. Given how small American and Loyalist militia regiments typically were in this campaign, Davie may simply be indicating that a Loyalist force consisting of hundreds of men must have included more than a single regiment. Sumter said that Bryan's was "the most considerable of the Tory encampments," clearly implying that some of the Loyalist militia were encamped elsewhere. Oddly, he indicated that the left British camp belonged to Joseph Robinson, an officer in the South Carolina Royalists, who was stationed at the British post at Ninety-Six, South Carolina. Sumter's statement could be read, though not very convincingly, to mean that the South Carolina militia were encamped there. Braisted, ibid., has Rugeley's militia defending one of the British guns after the Legion infantry was driven from the center camp. As the British forces were in considerable disarray at the time, it is more believable that both the Legion infantry and Rugeley's militia had been in the center camp than that Rugeley's militia came to their assistance from some other quarter. The Legion infantry and Rugeley's militia also appear to be the units stationed longest at this post. It's plausible that when they were first stationed at Hanging Rock, they chose to encamp near each other on the site of the center camp.