Yes, today is, or at least should be New Years Day. The start of the year, a holiday, a hangover, and a lot of closed shops — for a period lasting around 600 years, today was New Years Day.
Until 1752, Ladies Day was the first day of the year. So, in for example, 24th March 1689 was followed by 25th March 1690.
But in 1750, Parliament decided that the 31st December 1751 would be followed by 1st January 1752.
Although the 1st January was certainly celebrated as part of Yule, the main day took place on Lady Day, the first of the traditional four quarter days of the calendar.
It was Julius Caesar who originally set January 1st as the first day of the year, and England as a Roman province adopted that. Following the Norman Conquest, in 1087 the New Year was set on Lady Day, which fell on 25th March.
The reason being that it pretty much marked the beginning of the farming year, and was when workers might switch which farms they work at. So legal and employment contracts were exchanged then.
However, other countries later switched to the Gregorian calendar, and also had a different start of the year, causing confusion, especially for traders who dealt with Scotland or the rest of Europe.
Scotland for example, had switched New Year on 1st January 1600, so a contract signed in February would have different year dates depending on where it was enforced.
The Act for Regulating the Commencement of the Year; and for Correcting the Calendar now in Use, not only changed when New Year fell, it also abolished 11 days — thanks to the switch from the Julian to the Gregorian calendar.
As a result, Wednesday 2 September 1752 was followed by Thursday 14 September 1752.
That however had another effect, had the New Year not moved to the 1st January, the change of calendar would have shifted Ladies Day from 25th March to 6th April.
So today, the 6th April 2016 should be the first day of the year 2016.
The legacy of the Julian calendar still lingers on though — as today is indeed still the first day of the year — the tax year that is.