Let's get this right. It was not illegal to be or to practice Roman Catholicism in the UK up to 1829. Catholic Emancipation allowed full citizenship, ie holding of offices, attending university etc to Catholics. Catholics could attend Mass at embassy chapels, which were large and ornate. They could hold masses in private rooms - pub room services may have been in locked rooms for the same reason that Midnight Communion in the CofE church in Dover was done behind locked doors at New Year. There were nuns (I can't remember about monks and friars) from the late seventeenth century. Catholic need for hiding was a period of some 150 years from the time when the then pope proclaimed that it would be a good deed to assist Elizabeth I to enter the next life. Even then, there were court Catholics, such as the Norfolks, who were hardly hidden.
The reference I gave above, written by a Catholic, goes into more detail. Edward Norman, "Roman Catholicism in England from the Elizabethan Settlement to the Second Vatican Council", OUP, 1985, and is eye-opening.
I suspect that what has happened is that information from Ireland, the chief source of modern RC priests, where things were very different, has been superimposed on the English experience, which was not of such suppression, though there were wrongs, chiefly of differential taxation.
There was only a need of hiding things during the Commonwealth, when the last place you would hide doctrine would be in a secular Christmas song.