Most of the illustrations I've seen of the battle of Guilford Courthouse depict the British formed in two tightly packed ranks. In such a "close order" formation, each soldier in a rank occupies something like 2 linear feet.
Conversely, when an "open order" formation was used, a gap of about 18 inches or 24 inches (one arm's length) apart separated each soldier in a rank .
Given that detailed information is available on the British army at Guilford Courthouse , and having prepared a relatively detailed battlefield map, I thought it would be interesting to see how different the British army would have looked deployed in one formation instead of the other. For this exercise, I assumed that the British deployed in two ranks, that each soldier was about 18 inches across, and that 6 inches separated each soldier when they stood "shoulder to shoulder," while 24 inches separated each soldier when they stood in open order. 
Three maps are shown below. The first is based on a sketch made by a British officer shortly after the battle and it shows the British (in red) and American (in yellow) positions at the beginning of the battle. The two below that show, very roughly, the positions of the British (in red) and American (in blue) as the British advanced against the American first line. (This phase of the battle will be discussed at another time). On each of these two maps, the group of red lines at left depict the Guards Light Infantry company, a group of Jaegers (or Jäger), and the 33rd Regiment of Foot. Advancing through the fields are the 23rd Regiment of Foot, the 71st Regiment of Foot, and the Hessian Regiment von Bose. At far right is the 1st Guards battalion. In reserve is the Guards Grenadier company and the 2nd Guards battalion. At bottom (in column) are the British Legion dragoons.
If the Tarleton map (at top) is at all an accurate indicator of how the British were deployed, than surely a looser formation was used. By comparison, if the British stood shoulder to should it would have been quite impossible for them to come close to matching the breadth of the American line, except by leaving large, regiment-sized gaps between their units.
1. For an extended discussion of this and other tactical matters, see Matthew H. Spring's (2008) With Zeal and with Bayonets Only. The question of open and close order is also discussed at this website.
2. cf. Lawrence E. Babits & Joshua B. Howard (2009). Long, obstinate, and bloody: The battle of Guilford Courthouse.
3. Thus, the 23rd Foot, for example, with 238 men, has a front of about 238 feet at 6" file intervals and 417 feet at 24" file intervals.