In the British army, various dyes were used depending on the rank of the wearer. For officers, the most common dye was Cochineal, which produced a deep scarlet color. NCOs wore coats dyed true red, while the other ranks wore cheap madder, or brick red. (Myerly, 68) Coats were issued once yearly- Though it was common in the 18th century to continue wearing old clothing on the march, saving the new coats for parade and review.

On campaign, though, uniforms quickly deteriorated due to their often shoddy material and dye. Contemporary accounts make multiple references to dyes fading. The most common reference is to Infantry jackets aquiring a dusty hue. Cavalie Mercer, for example, wrote that Infantry mens' coats after the relatively brief Waterloo campaign, "...had faded to a dusky brick-dust hue..." (Mercer, 181)

Mercer's statement is echoed in Cuthbertson's "System for the Complete Interior Management of an Infantry Battalion," (rev. 1776), which complained that "The red breeches, usually given to the Infantry, in a very short time change to soot brick-color, and never have a clean appearance." Cuthbertson's reference to red breeches is likely a hold-over from an earlier edition- Red breeches had not been in use since 1768, when they were replaced by white ones. The "System" was more complimentary to those: "breeches of white cloth... have at all times a neatness in them, which is very pleasing to the eye; and they can, if ever so dirty, be recovered to their original whiteness..." (Cuthbertson, 72). White breeches, too, had their disadvantage- References exist to Dragoons in the Waterloo Campaign wearing breeches stained pink by the running dye of their jackets.

So, no- The uniforms frequently depicted in films such as Waterloo or Zulu are much brighter and well-maintained than they would have been in actuality.

Sources:

Cuthbertson, System for the Complete Interior Management and Oeconomy of a Battallion of Infantry (Rouths and Nelson, 1776)

Fletcher, Ian, Napoleonic Wars: Wellington's Army (Brassey's, 2000)

Mercer, Cavalie, Journal of the Waterloo Campaign, Vol. II (William Blackwood and Sons, 1878)

Myerly, Scott, British Military Spectacle (Harvard University Press, 1996)

While dyes don't reach "neon" standards until the late 19th century made possible with chrome dyes (heliotrope for example), some are rather bright and resilient. Colors that hold up to the sun; like red, blue, and green; are often preferable for military use. Within those there are numerous colors based on how they are dyed. Red has madder red, dyed with the madder root, and often used for the common soldier. It's cheap, stays well, but is a little more orange than the preferred scarlet for the officers (made with carmine). A variety of dark blues can be done with Indigo, something we are familiar with in our blue jeans even today. Greens (bottle, popinjay, grass, etc) are made with at least a two bath system, usually using indigo and yellow. Sometimes even having a chemical treatment in between like alum. Yellows come from boiling barks, though you see turmeric being used by the mid-19th century. There are drabs, browns, and greys found in some uniforms, but that plain coloring isn't the standard for military clothing until we see the change in warfare styles near the end of the 19th century.

I've worked with 18th century clothing and while some dyes are what we call "fugitive", changing color or fading over time, others hold on very well and brightly. George Washington's marquee tent he used during the war had red wool trim that is still bright scarlet. It saw decades of common use even after his death, but didn't bleach in the sun.

Check out the book Elephant's Breath & London Smoke by Deb Salisbury which has dated color descriptions going back hundreds of years. If you want to see modern color swatches for historic military uniforms look into Kochan & Phillips wool. There are a number of notes on that page about what color was used by what regiment, etc. Don't go too much by movies, they tend to have a color scheme in mind and will alter the image if need be to get the right "feel". For example, in your image they wanted a muddy, dirty feeling. Bright red doesn't add to that, so the soldiers wear grey blankets over their backs. It's not to say they didn't do that historically, it's just not their uniform".