The most commonly stated reason is that it would hide the appearance of blood on the battlefield, possibly demoralizing the troops.
Another good reason could be that British officers needed to be able to identify their men in heavy smoke.
A final possibility is that red is the primary color in the Royal Standard, the Royal Coat of Arms, and is the color of St George's cross (St George is the patron saint of England).
The German school focused on disciplined, close-drill order, well suited for the vast Central Plains of Europe.
After 1855, starting in India and gradually extending to other colonial outposts, the scarlet uniforms were often replaced with khaki on campaign for tactical reasons i.e. camouflage.