In contrast to some common misperceptions, the British army did not choose red because it hid the blood well. Instead the British army chose it because it was cheap. Blood would show up as a dark almost black stain on the cloth. Specifically, madder red. Madder does has an origin in the western parts of Asia and Egypt, and by the late seventeenth century the British army adopted it for their infantry coats. Due to trade expansions, the British merchants could get it easily. I will add that most of Europe had access to it for their cloth industry, not just the British. By this time the British woolen industry is really picking up steam as well. Not yet factories, instead it's cottage industry and a bit of specialization on the labor parts.

Now the British army did not just have one shade of red, but a few variations. The madder red is worn by the infantry's common ranks (privates and corporals), mock scarlet by sergeants, and scarlet by officers. Madder red has a more orange ish tint to it. I can link a picture of the variations to show it better. As I said before madder is cheap, but the others are more expensive. The cochineal red dyes come the shells of beetles from the New World. Still expensive but available. However, the Guard regiments would all wear cochineal based red coats. They were the premier units of the army and would have more expense for uniforms.

Why red? Let's go to the 1600s with the New Model Army by Oliver Cromwell. Cromwell wanted to standardize the army and created the uniform of a redcoat for the infantry. It was for ease of clothing, cost, and uniformity. Earlier infantry units had different uniforms and not all standard. With madder red being the cheapest and a government army needing to save funds for other expenses, it was an easy choice. The army had to cloth thousands of soldiers and doing so in blues, purples, or cochineal red would burst the budget before getting any other equipment.

Red was not the only color though. The British navy had blue, likewise with the artillery. Similar to the Guard units, the government would pull more funds for the uniforms of the navy or artillery than the regular infantry. Interestingly enough, the British army lost the royal distinction as a whole after the Cromwell wars, while the Navy and Artillery kept it. The guards are separate from that. This does not mean that the army did not have some royal distinction though. Certain regiments gained the honor of being a royal regiment and had distinct blue facings on their uniforms. Regiments such as the 7th Fuziliers, the 8th (King's Own) and 42nd Royal Highlanders (Black Watch) are just a few for examples. Facings were one of the ways to differentiate regiments among a sea of redcoats. They are the lapels on coats and ranged from blue, white, yellow, green, black, and even red. With the 1768 Royal Warrant, coats would also be ordered to have lace on their coats and every regiment usually had their own. Coats in the Seven Years War did have lace but not usually a distinct type.

While red seems like a British color, it was not always so. During the French & Indian War and the American War of Independence, the British army also had provincial units under their command and most had different color coats. Greens, Browns, and Blues were common cloth colors for them. Units such as Rogers' Rangers and Butler's Rangers had green, same with Queen's Rangers and British Legion. It did give them distinction on the field and as a unit. Now I said this for the provincial units of the British army, but one regular British regiment in the F&I war did not have red. The 80th Regiment of Light armed soldiers had brown. Light infantry was in it's beginnings in the Seven Years War and the F&I war. Brown coats, waistcoats, breeches, and leggings were thought to help with guerrilla type fighting. I've posted before on the non-linear warfare tactics of the British army before, I'll link it too. So while the British army had standardized, they were willing to adapt to conditions. Oddly enough, green somewhat does not help would with camouflage, at least not a solid color, but I digress.

The French primarily had white uniforms but there are some regiments that have blue or even redcoats. The artillery had blue uniforms faced with red. Blue as an artillery coat color was common among the European nations. The white coats would have different colors on cuffs, collar, and lining as well. Ranging from blue to red. To add to the white uniforms, the Spanish also chose this color for their coats. The "Germanic" states also had their own color for coats, often called Prussian or Hessian blue. I say Germanic since the country would not be founded until way late in the nineteenth century. In the 18th century, the area of Germany consisted of separate territories such as principalities, Prussia, and the Holy Roman Empire. It's a bit more complex than that but I do not want to digress too much.

I would argue that in some cases, the nationalities would have a distinct color for their coats but not always as seen above. There are some iconic images of the uniforms of the era such as the redcoat and the white for France due to popular media. The reasons for it were not always because of nationality but for cost. Later on it might have became part of a national army image.