If you look in your ancient but admirable English Missal, you can find our Lady as Mediatrix of all Graces in the Appendix of Masses Proper to England and Wales. This is because in Durham, Northumberland, the West Riding of Yorkshire, Herefordshire, and all Wales, this feast was on the Calendars of the corresponding RC dioceses. The date is May 31, except that in later editions of the English Missal, printed after the institution in 1955 by Pius XII of the feast of the BVM, Queen, on May 31, the older feast of our Lady, Mediatrix, had to be shuffled onto June 1. (The Mass can, of course, be said as a votive any day when votives are permitted.)
Happily, one of the Office Hymns of this beautiful Feast appears in the Liturgia Horarum. In the Common of the BVM, it is the hymn at First Evensong; and it may be used at the Office of Readings as an alternative to Quem terra pontus aethera. Its first line is Maria quae mortalium.
Sadly, for those who say the Office in English, it is not available; it is one of the many hymns for which ICEL decided not to bother to commission English translations. (Whereabouts did Sacrosanctum Concilium mandate this wholesale disparagement of the treasures of Christian Latin Hymnography?) It may be found, with an English version, in versions of the Monastic Diurnal for the Feast of our Blessed Mother of Perpetual Succour. Its (nineteenth century) author is not known.
The Mass and Office for our Lady Mediatrix of All Graces were authorised in 1921 by Pope Benedict XV, and among the countries for which they were authorised was Belgium. The Feast had been requested by that dear friend and supporter of ecumenical dialogue with the Anglican Patrimony, Cardinal Mercier, Archbishop of Malines, him of the 'Malines Conversations'. Perhaps we ought to make Mercier and Malines more prominent in our recollections of the pre-history of the Ordinartiate!
It is my instinct that Papa Pacelli in 1955 deliberately put Maria Regina on May 31 because his own Marian preoccupations had other priorities which rather overshadowed her title as Universal Mediatrix. Did he wish to discourage the growing enthusiasm among dioceses and countries to petition for this feast? But Wales and the ancient, mighty See of Hexham had got in first!
So the whole Latin Church has now ended up with either Maria Regina (EF) or the Visitation (OF) today, the last day of the Marymonth. I feel the Pius XII (EF) propers are a trifle unsophisticated; they emphasise the old literary topoi of Royalty. No harm, I suppose, in that ...
... But the older liturgical understanding of Mary's glorification, in both West and East and Further East, connected it with her role as Mediatrix for all the Church. The only element in the Pius XII office which directly relates to this theme is lectio ix, where S Bonaventure proclaims Mary as the New Esther and as the aquaeductus through which the Grace of God comes to us.
On the other hand, the Benedict XV propers very neatly and ecumenically brought the Semitic, Hellenic, and Latin traditions of Christianity together, especially in the Second Nocturn (a lection each from S Ephraim, S Germanus Patriarch of Constantinople, and S Bernard). And the use of Typology is richly suggestive; very much in line with the Mariological perspectives which S John Henry Newman came to discern in his last weeks as an Anglican.