The Golden Legend, by Archbishop Jacobus de Voraigne of Genoa, published between 1260 and 1275, and printed many times (once printing was invented), was a medieval best seller. It included the lives of many saints and much other information. It states that the Annunciation and the Crucifixion, and several other events, happened on March 25th. The popularity of this book would be sufficient to account for the popularity of this belief in the later Middle Ages. There may, of course, have been other sources too.
This passage is translated:
This blessed Annunciation happened the twentyfifth day of the month of March, on which day happened also, as well tofore as after, these things that hereafter be named. On that same day Adam, the first man, was created and fell into original sin by inobedience, and was put out of paradise terrestrial. After, the angel showed the conception of our Lord to the glorious Virgin Mary. Also that same day of the month Cain slew Abel his brother. Also Melchisedech made offering to God of bread and wine in the presence of Abraham. Also on the same day Abraham offered Isaac his son. That same day S. John Baptist was beheaded, and S. Peter was that day delivered out of prison, and S. James the more, that day beheaded of Herod. And our Lord Jesu Christ was on that day crucified, wherefore that is a day of great reverence.
So, according to this legend, the Creation of Adam, the Fall of Adam, the murder of Abel, Melchisedech's offering of bread and wine, Abraham's near sacrifice of Isaac, the Annunciation to Mary and Conception of Christ, the decapitation of John the Baptist, the Crucifixion of Christ, James' killing and Peter's escape all occurred on March 25th.
The matching dates for Annunciation and Crucifixion are referred to , around 400, by Augustine in Book 4, Chapter 5, of his work on the Trinity:
For He is believed to have been conceived on the 25th of March, upon which day also He suffered; so the womb of the Virgin, in which He was conceived, where no one of mortals was begotten, corresponds to the new grave in which He was buried, wherein was never man laid, neither before nor since.
This is likely the source for the dates in the Golden Legend.
It is said that there was a tradition that great prophets were conceived and died on the same day. Moses announced on what appears to be his last day :
"I am an hundred and twenty years old this day". Deuteronomy 31 2. This is known as the integral age concept, which however does not seem well corroborated.
With regard to the Sarum calendar, this article states that the inclusion in liturgical calendars of several historical dates was very common in the middle ages. The most common listing is for the Resurrection, which if listed is always on March 27th. This is further corroboration of the popular belief that the Crucifixion and the Annunciation took place on the same day, and that this belief was recognised in church calendars.
March 27th was listed as the historical date that the Resurrection occurred. It had no effect on the date of the Easter celebration.
Some additional support may possibly be inferred from the old Scottish Quarter Day on May 15th which was known as Whitsunday. May 15th is exactly 7 weeks after March 27th. The usual meaning of Whitsunday is Whit Sunday (known in some countries as Pentecost), as mentioned here, but for various purposes in Scottish law (e.g. moving house) was formerly regarded as fixed. If the Resurrection occurred on March 27, the Descent of the Holy Ghost, which is the event marked at Whitsun, would have been May 15th.