Most western European countries changed the start of the year to January 1 before they adopted the Gregorian calendar. For example, Scotland changed the start of the Scottish New Year to January 1 in 1600. England, Ireland and the British colonies changed the start of the year to January 1 in 1752. Later that year in September, the Gregorian calendar was introduced throughout Britain and the British colonies. These two reforms were implemented by the Calendar (New Style) Act 1750.
It is interesting to read. I never thought much about it before. I knew there were other "calendars" and other New Years, but I learned something. Pretty cool.