The "g" never completely left England in the first place. It was one of several spellings. 

For example, the first full English translation of the New Testament, from the Latin Vulgate rather than the original Greek,  was the [unofficial translation][1] by Wycliffe in 1382.  In the space of 11 verses (Matthew  27  verse 56 to 28 verse1) Wycliffe  spelt the name  three different ways: "Magdalene", "Maudelene" and "Mawdelene".   

Chaucer  also used spellings with and without the g.  King Henry VII (reigned 1485 - 1509)  wrote to the Oxford college spelling its name with a"g",  and Henry VIII used various spellings. [Reference][2]

Mary Magdalene was said to have lived in France for many years, and there are many stories and legends about her time there.  Some even suggested she may have been "Mrs Jesus". Her cult was especially popular in France, and with the Normans who conquered England. Also the Knights Templar held her in great regard.   The first "a"  in Magdalene was pronounced in England similar to in France,  to rhyme with  ball and water. Said this way the "g" sound virtually disappears, and this is the reason for it often  being omitted. 

The Gospels tell us that Mary Magdalene  accompanied Jesus on a preaching tour (Luke 8), and may have provided financial support. She was present at the Crucifixion and was the first person known to have met Jesus after the Resurrection (e.g. Matthew 27 and 28, Mark 15 and 16; John 19 and 20). It was she who told the male disciples Christ had risen, though they did not believe her until they saw for themselves. 

The  Gospels also refer to a Mary at Bethany (John 11), sister to Martha and Lazarus; and to a  penitent "sinful woman" whose tears wet Jesus' feet, which she then dried with her hair (Luke 7). The early Church had long speculated that these two women and Mary Magdalene were all one and the same person, and Pope Gregory in the sixth century asserted  this was so. This is known as the Composite Magdalene.  The portrayal  of Mary Magdalene as weeping and sentimental (washing Jesus' feet with tears as well as moping about in the garden after His death) led to her association with weeping sentimentality and to our word "maudlin".

The sixteenth century saw several mass-produced Bibles in English, beginning with Tyndale's illegal translation in 1526.  The first official English Bible, the Great Bible of Henry VIII,  was produced in 1539, and copies placed in every parish church. The Geneva Bible was produced abroad during Queen Mary's reign  (1553 to 1558) , and very widely circulated when Elizabeth succeeded her. Another official version, the Bishops' Bible was produced in 1568, followed by the King James Version of 1611. All these  Bibles agreed in spelling  Magdalene with a "g".  Indeed the original Greek word, which  begins mu-alpha-gamma-delta, pretty much mandated this.  

As spelling became standardised the standard spelling of Biblical names naturally conformed to the spelling used in  Bibles.  This applied to Oxford and Cambridge colleges as to everyone else. We will not find a decision by the colleges to officially change the way they spelt their names, with effect from a certain date, because spelling wasn't consistent or official to begin with. 

It is possible that the  older pronunciation would have lasted longer if her cult had persisted. The Reformation reduced the role of saints generally. They were no longer prayed to. Although the feast days of the male disciples were retained,  Mary Magdalene's was cancelled, lingering only as a note in the Church of England calendar, but with no special prayers or readings. The identification of Mary Magdalene with Martha's sister and the tearful penitent was dismissed as papal speculation. The French legends were of no further interest.  To Protestant England, "Mary Magdalene" was simply not the woman she used to be. At most, she was one facet of her former persona. As the first witness of the Resurrection she was still a saint, but people largely lost interest in her. Calvin even went so far as to call her  foolish and unspiritual, and saw Christ's appearance to her first as a reproof to the men,  who deserved to be taught by oxen and asses, never mind women! Had she retained her place in popular devotion she might well have retained her pronunciation, due to constant use. As it was, her name was pronounced, when read,  as written.

This [paper][3] by Frank Henderson explores the dropping of her feast day in England, and considers he attitudes of the Reformers generally. 

Very commonly where a name becomes a word, as maudlin did, the word takes on a separate existence independent of the person. In this particular case Mary Magdalene was no longer definitively identified with the weeping penitent woman anyway, so there was even less reason why the word maudlin should follow the Biblical pronunciation, or spelling, of Magdalene.

As regards the colleges the pronunciation stuck the way many place names stick, because people see no need to change them, especially from two syllables to three or four.   There may also at times have been be an element of academic pride, or shibboleth.