Why 1 January?
The Romans derived the name for the month of January from their god Janus, who had two faces, one looking backward and the other forward. Britannica
Janus, in Roman religion, is the animistic spirit of doorways (januae) and archways (jani). Britannica Some scholars regard Janus as the god of all beginnings and believe that his association with doorways is derivative. Britannica The beginning of the day, month, and year, both calendrical and agricultural, were sacred to him. Britannica
The month of January is named for him, and his festival took place on January 9, the Agonium. Britannica Janus was represented by a double-faced head, and he was represented in art either with or without a beard. Britannica
On the Roman republican calendar the year began on March 1, but after 153 BCE the official date was January 1, which was continued in the Julian calendar of 46 BCE. Britannica
In early medieval times most of Christian Europe regarded March 25, the Feast of the Annunciation, as the beginning of the new year. Britannica New Year's Day was observed on December 25 in Anglo-Saxon England. Britannica William the Conqueror decreed that the year begin on January 1, but England later joined the rest of Christendom and adopted March 25. Britannica
The Gregorian calendar, adopted in 1582 by the Roman Catholic Church, restored January 1 as New Year's Day. Britannica Britannica says most European countries gradually followed suit, for example Scotland in 1660, Germany and Denmark about 1700, England in 1752, and Russia in 1918. Britannica
When did Scotland make 1 January the official New Year?
Encyclopaedia Britannica's New Year festival article says most European countries gradually followed the Gregorian restoration of 1 January, and gives Scotland in 1660 as an example. Scotland's People, the official family-history site of the National Records of Scotland, says the first official New Year which took place on that date in Scotland was 1 January 1600, and that before then the year officially began on 25 March. The Calendar (New Style) Act 1750 later recites that England's legal year still began on 25 March, and that this differed from the legal method of computation in Scotland. We report both dates and do not treat 1660 as settled.
According to Scotland's People, the first official New Year which took place on 1 January in Scotland was 1 January 1600. Scotland's People Before then, the year officially began on 25 March. Scotland's People The rest of the British Isles did not adopt the New Year change until 1 January 1752, by which time 11 days had to be removed from the calendar in adjustment. Scotland's People
The Gregorian calendar is a solar dating system now in general use. It was proclaimed in 1582 by Pope Gregory XIII as a reform of the Julian calendar. Britannica By the Julian reckoning, the solar year lasts 365 1/4 days. Britannica The solar year more precisely lasts 365 days, 5 hours, 48 minutes, and 45.25 seconds, that is, more than 11 minutes shorter than 365 1/4 days. Britannica This slight inaccuracy accumulated and caused the calendar dates of the seasons to regress by almost one day per century. Britannica
Although this regression had amounted to 14 days by Pope Gregory's time, he based his reform on restoration of the vernal equinox, then falling on March 11, to March 21, the date it occurred in 325 CE. Britannica The change was effected by advancing the calendar 10 days after October 4, 1582, the day following being reckoned as October 15. Britannica
Within a year the change had been adopted by the Italian states, Portugal, Spain, and the Roman Catholic German states. Britannica Gradually, other countries adopted the Gregorian calendar: the Protestant German states in 1699, Great Britain and its colonies in 1752, Sweden in 1753, Japan in 1873, China in 1912, the Soviet socialist republics in 1918, and Greece in 1923. Britannica Countries that switched later had to drop more days: Great Britain dropped 11 days in 1752, and Greece dropped 13 days in 1923. Britannica
The British statute is the Calendar (New Style) Act 1750 (24 Geo. 2 c. 23). Calendar Act 1750 The Act recites that the legal supputation of the year of our Lord in England, according to which the year beginneth on the twenty-fifth day of March, had been found inconvenient. Calendar Act 1750 It also notes that this English reckoning differs from the legal method of computation in Scotland. Calendar Act 1750
From and after the last day of December 1751, the first day of January following was to be accounted the first of the year 1752. Calendar Act 1750 The natural day next after 2 September 1752 was to be accounted 14 September, omitting for that time only the eleven intermediate nominal days of the common calendar. Calendar Act 1750
England's legal year, in the Act's own wording, still began on 25 March until that change. Scotland already reckoned the year from 1 January, which is why the Act mentions a difference between the two.