The numbering and facing system is extra complicated in the UK and probably other European armies because it's a direct and continuous evolution from the feudal system.
From the Wars of the Roses the professional military of the UK was entirely within either the royal guard or noble retinues, intended to be backed by trained bands of militia, and none of these groups had any real uniforms beyond whatever personally relevant symbols and schemes appealed to the commanders and owners of the organisation, and in the case of the bands, armament quotas (a mix of longbows and billhooks at the beginning of the 16th century, with orders to transition to pike and shot quite early on somewhere between mid-century and the 1580s, but supply issues meaning that the changeover was only completed shortly before the civil wars).
Identifying markers similarly were up to the commander and there was no concept of the "king's colour" and the "regimental standard", rather having, among many others, the Colonel's Colours and the Captain's Colours for each company. The civil wars saw a free-for-all in terms of fashion and organisation, culminating in the new model army. Cloth cut and colour as well as facings began to be standardised but the organisational structure was still fundamentally medieval- Until a set of major reforms in the mid-late 18th century which introduced numbered regiments and standardised colours (standards), each regiment was known by the Colonel's name, causing a lot of confusion and extra paperwork every time the commanding officer changed.
About another century later the Cardwell Reforms changed regimental titles to County Names, although some kept their numbers as well for prestige reasons.
There have been multiple reforms since then expanding and contracting the army dependent on need (ex during the first world war regiments went from 1-2 battalions each to 14-20+). The main changes of the 20th and 21st centuries are continued downsizing and amalgamating as, from the top down, the traditions and heritages of the army are stripped away.
Retaining traditions is an important and enduring part of the british army which introduces endless complications that persist to the present day- iirc the Surreys have a bit of extra piping or tape on the back of their collars which is a vestigial remnant of their 1685 uniform which incorporated a large bow in their queued hair, which rested in the same position and served to keep flour from their powdered hair from dusting too much of the jacket.