Most modern armed forces have numerous uniforms for the various different environments and situations they will be expected to operate in. In the case of the British Army, there are twelve numbered orders of dress as well as Full Dress.

Your question is referring to Full Dress. These are the most ornate uniforms and are only used on the most important ceremonial occasions. None of these uniforms date from the Napoleonic era. Rather, they tend to be as they appeared in the very early years of the 20th century, just before the First World War. All Full Dress includes features which developed after 1815, most particularly in terms of headdress but also in the cut and style of jackets/tunics, the types of trousers and footwear, and the dress distinctions of the different corps and regiments in terms of buttons, facings and other distinguishing marks.

This question is further complicated by the fact that many of the corps and regiments of the British Army have come into existence relatively recently. This is most obvious in terms of the line regiments of cavalry and infantry, most of which have only assumed their current forms in the last couple of decades after several amalgamations and disbandments since the late 1950s. The dress distinctions of these newly-formed regiments are designed to take into account the uniforms of the predecessors, which may in turn also have been designed in the same way. On that basis, the majority of the British Army's Full Dress has been developed in the late-20th and early-21st century, albeit within a framework which dates back around 100 years. So, you could say that Full Dress is modern, but largely inspired by late-Victorian military dress.

In terms of your specific question about "honor guards", the Full Dress uniforms of the Household Division (the two regiments of Household Cavalry, and the five battalions and three incremental companies of Foot Guards) and the King's Troop, Royal Horse Artillery are relatively unusual in the context of the wider British Army. Firstly, they wear their Full Dress much more often than the rest of the British Army. The Household Division provides a single mounted regiment, two battalions and three incremental companies of Foot Guards at any one time to conduct ceremonial duties. These will wear Full Dress whenever they conduct ceremonial activity. For wider context, the personnel of these elements are full-time combat soldiers who are rotated in and out of these ceremonial roles as part of their standard military duties.

Because of the nature of their role, these elements of the Household Division are provided a full set of Full Dress uniforms at public expense. In the rest of the British Army, the wearing of Full Dress is so unusual that only limited numbers are provided at public expense and most need to be provided from within regimental funds, ie: money raised by the regiment, not provided by the government. Those which are provided are usually for musicians and guards of honour.

You're also wrong to associate red with the dress uniforms of the modern British Army. The Full Dress of most infantry regiments includes a scarlet tunic, but blue and green is worn by the Royal Armoured Corps, Royal Artillery, Royal Engineers and rifle regiments. Other arms and services also wear blue, not red.

The other ornate ceremonial uniform in the British Army is No. 1 Dress, or temperate ceremonial dress. The majority of the British Army wear blue or green jackets in this form of dress, not the red of popular imagination. This form of dress only dates to the 1930s and is only worn on very formal ceremonial occasions. As with Full Dress, it is not widely issued.

The main formal and parade uniform is called No. 2 Dress, and features khaki uniforms which are directly inspired by the Service Dress uniforms first issued in around 1902. All soldiers are issued No. 2 Dress and it is what you will see most British soldiers wearing in routine ceremonial situations.