Was it possible for Catholics to express their faith openly in England during the time of persecution?

Yes, sometimes more freely than others. Laws like this will always be patchily enforced. If the local landowner was a Roman Catholic, as many were, or if the king was Roman Catholic (as James II), or if the authorities lost interest in suppressing Roman Catholicism, then Roman Catholics could be fairly open, but other times they had to be more secret.

They sang "The Twelve Days of Christmas" as an expression of faith and quite openly!

In 1870, the song of The Twelve Days of Christmas was first published in England, shortly after the time when it was a criminal act to practice the Catholic faith. According to the Tridentine Mass of Pope Pius V (1570), the Christmas season lasted from the Solemnity of the Birth of Our Lord until the Feast of the Presentation of Our Lord, on February 2 (40 days). However, the Liturgical Year counted Sundays as being in the time of the Epiphany, instead of ordinary time as we do now, thus making the “Twelve Days Of Christmas” to be taken as being from the Solemnity of the Birth of Our Lord until the Vigil of the Epiphany (January 5). The Twelve Day of Christmas carol had a totally different historical meaning for the faithful living in Britain during the persecutions against Catholics from April 29, 1559 to April 13, 1829 (Roman Catholic Relief Act 1829), when it was a criminal offence to practice the Catholic religion. Catholicism remained illegal for some 232 years. The singing of this carol was a way for persecuted Catholics to express their faith openly in England as laid out in the twelve points in the Apostles’ Creed.

Being a time of persecution, the faithful would naturally not have any written works on its' real interpretation in order to avoid linking them to the Catholic Church.

None of the numerated parts of the song could be used to distinguish Catholics from Anglicans (or Protestant for that matter), and could thus be sung quite openly as an expression by the faithful of the Catholic Church.

Other interpretations do exist for numerated parts of this carol as to the symbolism they meant to Catholics living in England during the persecutions for their faith. None other than the Apostle’s Creed interpretation makes this a uniquely Catholic carol sung at Christmastide. Here is the most popular interpretation of “The Twelve Days of Christmas.”

1. The partridge in a pear tree is Jesus.
2. The two turtledoves are the Old and New Testaments.
3. Three French hens stand for faith, hope and love.
4. The four calling birds are the four Gospels.
5. The five gold rings recall the Hebrew Torah (Law), or the Pentateuch, the first five books of the Old Testament.
6. The six geese a-laying stand for the six days of creation.
7. The seven swans a-swimming represent the seven gifts of the Holy Spirit.
8. The eight maids a-milking are the eight Beatitudes.
9. Nine ladies dancing are the nine fruits of the Holy Spirit.
10. The ten lords a-leaping are the Ten Commandments.
11. Eleven pipers piping represent the eleven faithful Apostles.
12. Twelve drummers drumming symbolize the twelve points of doctrine in the Apostles Creed.

Here is “The Twelve Days of Christmas” sung on YouTube: “The Twelve Days of Christmas” - Hayley Westenra, Russell Watson, Aled Jones (Songs of Praise).

In 1982, Fr. Stockert put this online in 1982. Since then there has been controversy on whether or not the story of the origin is correct. Much of the story makes sense, because there are other "Catechism songs" that have similar hidden meanings, such as "Green Grow the Rushes". Could some people be disputing the origin because they refuse to acknowledge the persecution of Catholic in England during 1558 to 1829? Perhaps the objection is just to the fact that there is no paper trail to this explanation. Regardless if the origin is accurate or not, as Catholics we can use this song as a catechism, to apply religious meanings to a secular song. - Origin of the Twelve Days of Christmas