Catholics must "accept their calling" to be "out of step with popular culture" and "to live faithfully by the teaching we have received," said the document, titled "The Narrow Gate."
The bishops suggest how Catholics should behave following passage of the Marriage (Same-Sex) Couples Act, which became law July 17 and opened the door for same-sex marriages to occur as early as summer 2014.
The document was written and signed July 6 by Archbishop Vincent Nichols of Westminster, president of the Bishops' Conference of England and Wales. It presents Catholics with a mandate on how they should respond to a law which, the archbishop said, creates a sense that they are "strangers in their own land."
Upholding church teaching that all sexual activity outside of the legitimate marriage of one man and one woman is sinful, the document stressed that marriage is a lifelong, faithful commitment "ordained by nature and by God for the creation of the family and future generations."
"It is clear that the Catholic Church cannot accept the validity in church law of same-sex marriages," the document said.
The law represents "the deconstruction of marriage as it has been understood for millennia" and "completes the privatization of marriage, so that its central content is whatever the couple wish to construct," the document said.
"Marriage is no longer a truly public institution, at the basis of society. In passing this act, with widespread support among sections of our population, our society has taken a significant step away from its Judeo-Christian foundations," the document said.
"Marriage is the place where sexual relations find their proper place and God-given purpose. Both as a natural, human institution and as raised by the Lord to the dignity of a sacrament, marriage provides the best circumstances for the birth and nurture of children and forms the most reliable links and supports between the generations," it said.
The document acknowledged that the "intrinsic link between sexual relations and the procreation of children has in practice long been abandoned" and that there are other areas where church teaching conflicts with social norms.
"We try to present and live by Catholic teaching as given by God for the ultimate good for each person. This may indeed lead us to feel, in these matters, out of step with popular culture. But that is our calling and not a matter for discouragement. Rather, with the confidence of faith, we stay resolute, encouraging one another and all who recognize the values we wish to uphold," the document explained.
"Our place as followers of the Lord is not fashioned for our comfort. But nor is our discomfort something about which we should complain," the document added. "From the outset until today, the Lord's call to follow him has meant standing apart, quite clearly in some times and places. However, that apartness is neither separation from nor disdain for our society."
The document suggested three principles to guide Catholics in their dealings with their families, with other Christians and with wider society.
The first is to "robustly and intelligently" present the teaching of the church on marriage, primarily through the faithful witness of their own lives.
The second is to "make every effort to accompany one another through the difficulties and trials of life," especially with prayer and regular reception of the sacraments.
"The third principle is that we are always willing to engage in dialogue and conversation with those who see things differently," the document said.
In the Diocese of Shrewsbury, in northwest England, Bishop Mark Davies has written an accompanying pastoral letter that was to be read during weekend Masses.
"We are facing together a completely new situation which invites us -- with growing urgency -- to engage in a 'new evangelization' and a courageous lay apostolate," Bishop Davies said in the letter.
He warned parishioners that by remaining faithful to church teaching they may be accused of bigotry or of embracing an "outmoded understanding of human relationships."
But the bishop said he has "no doubt that it is through such witness -- your own witness -- that the Christian foundations increasingly discarded by the leaders of our society will be discovered anew."