St John Fisher was executed on 22 June 1535, and Thomas More on 6 July.
Wikipedia has an interesting paragraph on the significance of the date of Fisher’s execution…
However, a public outcry was brewing among the London populace who saw a sinister irony in the parallels between the conviction of Fisher and that of his patronal namesake, Saint John the Baptist, who was executed by King Herod Antipas for challenging the validity of Herod’s marriage to his brother’s divorcée Herodias. For fear of John Fisher’s living through his patronal feast day, that of the Nativity of St John the Baptist on 24 June, and of attracting too much public sympathy, King Henry commuted the sentence to that of beheading, to be accomplished before 23 June, the Vigil of the feast of the Nativity of St John the Baptist. His execution on Tower Hill on 22 June 1535, had the opposite effect from that which King Henry VIII intended as it created yet another parallel with that of the martyrdom of St John the Baptist who was also beheaded; his death also happened on the feast day of Saint Alban, the first martyr of Britain.
St John Fisher[Wikipedia]