The Roman rule with respect to Orthodox saints venerated by Eastern Churches coming into union with Rome is that they may all be kept save for those who have been vocally against Rome during their lives.
Thus, St Mark of Ephesus or the Athonite Martyrs of Zographou burned by the Emperor for refusing to come under Rome would not be acceptable for EC liturgical veneration.
Although Patriarch Photius has been villified in the West, he is making his way into the calendars of EC churches (and Fr. F. Dvornik’s work on him has helped in this process).
Sts Vladimir and Olha, for example, were canonized by the Orthodox Church but are honoured not only by EC churches but by Rome as well where in the Roman calendar they are listed under their baptismal names: Vasyl/Basil for Vladimir, Helen for Olha (and Romanus and David for Sts Boris and Hlib).
Rome has acknowledged the sainthood of St Gregory Palamas and some other Orthodox saints (especially St Seraphim of Sarov).
There are EC parishes that venerate all the Saints of Orthodoxy, even the newer saints as they are canonized (save for the exceptions noted above).
The Anglicans honour Blessed King Charles the Martyr as the only saint they’ve canonized since the Reformation. The convocations of York and Canterbury declared him a Martyr in the 17th century and established a feastday for him and office propers. January 30th was formerly a fast day for the sin of regicide.
The Anglicans also have local worthies whom they will title “Blessed” such as Nicholas Ferrar, William Laud, Lancelot Andrewes, William Law, Edward Pusey, James DeKoven and others. Anglicans will also often list in their calendars the names of English saints whose canonization processes were stalled and never completed such as King Henry VI, John Schorn of Buckingham and Richard FitzRalph of Dundalk.
(As an aside, Fr. John Schorn was known to work miraculous cures for the gout. His local veneration in the Middle Ages led to the creation of statuary of him pointing to a boot out of which a devil’s head was popping out. This was the origin of the toy, “Jack in the Box.”)
The form of commemoration of these will be different based on the “High, Middle and Low” Anglican church polity and traditions.
I understand that the Anglicans seeking union with Rome via the Ordinariates are calling on Rome to regularize their liturgical veneration of Bl. Charles, King and Martyr (and why shouldn’t it?).
Blessed John Henry Newman and Ronald Knox as well as other notable Anglican converts to Catholicism continued to privately venerate Bl. Charles the Martyr. Knox actually wrote a formal letter to Rome calling for the canonization of King Charles I (and King Henry VI). Veneration of both kings was a hallmark characteristic of the Oxford Movement and continued with RC converts from this movement.
I am myself a member of the Society of King Charles the Martyr.
Alex