Um, Setanta, here's pretty much how it was taught at my school:
Source
Using the year of Christ's birth as a method of dating was not originated by Bede (that honour can be claimed by a monk resident in Rome, Dionysius Exiguus, c.525), but his adoption of the system ensured its popularity. It is widely (though not universally) accepted that, in his 'Ecclesiastical History' (since he was dealing with documents using an earlier form of reckoning), Bede chose to begin each year in September (preceding the 1st of January which would now define the beginning of the year), and acceptance of this convention does remove some, though not all, chronological inconsistencies within the work. At any rate, not unreasonably, the use of Christmas Day as the starting point for the year was soon in vogue. However, from a theological point of view, it was thought that the 'Feast of the Annunciation' (25th March) would be more correct, and, in England for instance, by the late 12th century, the succeeding 25th March (even though logic would dictate that it should be the preceding March - as indeed was espoused elsewhere) was in common use as the beginning of the year. Different conventions were adopted across Europe. R.L. Poole writes:
"If we suppose a traveller to set out from Venice on 1 March 1245, the first day of the Venetian year, he would find himself in 1244 when he reached Florence: and if after a short stay he went on to Pisa, the year 1246 would already have begun there. Continuing his journey westward, he would find himself again in 1245 when he entered Provence, and on arriving in France before Easter (16 April) he would be once more in 1244."
Following the reforms of the calendar authorised by Pope Gregory XIII in 1582, there began the process of adopting 1st January as the beginning of the year. Scotland fell into line on 1st January 1600, but in England, Wales and Ireland, the change was not effected until 1st January 1752.