A while ago, I saw a comment somewhere (not necessarily fedi) that boiled down roughly to this:
"The British aristocracy made their (edit: male) servants recognisable as such by dressing them in formal clothes, but in mismatched combinations (i.e. tailcoat with a black bowtie, long tie with a wing collar)."
This was (roughly speaking and to the best of my knowledge) about the Victorian through Edwardian and early Modern periods, i.e. when formalwear as we know it (morning coat, tailcoat, etc.) already existed in roughly the form we know it.
I can't find that comment anymore, and I don't expect I ever will, but it would be fascinating to read more about this subject, very specific and niche as it is. I've tried googling around for it (i.e. "historical british servant dress codes"), but found very little.
If anyone has some reading material on that (preferably online or books buyable online, if not I'll have to see if my library can get foreign (english) literature), I would be super grateful for any links or the likes.
I would start with the Tudor period and work to the Victorian. The Tudor sumptuary laws may contain sections/clues on livery that you can trace forward to Victorian and Edwardian periods.