The regulations, in 1768, before, and since, are the result that, since the 17th century, red has been part of the royal livery of Britain, the King (or Queen) of England's own livery being lined with blue. Hence the government's soldiers, being servants of the Crown, would wear red coats. Those regiments most distinguished might have red coats with blue linings (and facings) as a sign of royal approbation from the monarch. Scots regiments tended to have red coats with yellow lining, following the old livery of Scotland, red and yellow, after the Union of 1707. Red continues to be worn in full dress by many troops in the United Kingdom, Canada, Australia and other countries of the Commonwealth.
Britain is not the only nation to have red livery. So does Denmark and its troops also wore red, as did Poland for a time and some German principalities. In some countries, notably France and Spain, the King's livery was blue lined with red but his Queen's livery was the reverse colours, red lined with blue, so that the regiments honoured by the Queen's title and approbation would have the honour of dressing their regiments, or at least their drummers, in red coats.
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