On 25 March, the Church celebrates the announcement by the angel Gabriel to Mary that she would become the mother of Jesus. The celebration is referred to as the Feast of the Annunciation, or traditionally as Lady Day. In England, Lady Day was New Year’s Day up to 1752, when England moved from the Julian to the Gregorian Calendar. The Gregorian is the calendar widely used in our present days, and this calendar marks 1 January as New Year’s Day. The reason of using 25 March as the start of the year is that it roughly coincides with Equinox, namely the date when the length of day and night is equal.
In his “The Lord of the Rings”, J.R.R. Tolkien recorded that the Ring (the main antagonist in the story) was destroyed, and thus Middle-earth was saved from destruction, on a 25 March. Tolkien further emphasized (through Gandalf) that from then on, a new year would begin on 25 March, as a testimony to the great significance of the destruction of the Ring. As Tolkien conceived his Middle-earth stories partly due to his opinion that his homeland, England, lacked a mythological identity, it was no surprise that he deliberately chose this date. And of course there is no doubt that he deliberately chose the dates. When one conceives a mythology for a land, it has to fit some of the details of that land, I guess.
Update: I just found that Tolkien Reading Day is also celebrated on 25 March! (as if I needed further encouragement to read Tolkien).