The cardinal warns that Britain shows signs of degenerating into a country free of morals, because of its rejection of traditional values and its new emphasis on the rights of the individual.
There are now "serious tensions" between Christians and secularist society, he says, in which atheists are becoming more "vocal and aggressive".
Writing in a book on multiculturalism, to be published tomorrow, the Cardinal argues that immigrants have a duty to adjust to British life, but expresses concern that they are faced with a culture that is increasingly repressive and intolerant. He says that while the country has become more diverse and pluralistic, the Christian values which have shaped its identity should not be abandoned.
The book, called Faith in the Nation, is published by the Institute for Public Policy Research (IPPR), with the backing of the Prime Minister. In it the cardinal says: "Religious belief of any kind tends now to be treated more as a private eccentricity than as the central and formative element in British society that it is.
"Although the tone of public discussion is sceptical or dismissive rather than antireligious, atheism has become more vocal and aggressive."
Britain's most senior Catholic leader says that the "unfriendly climate for people of all faiths" has united the country's three major faiths, Christianity, Judaism and Islam. However, he claims that Catholicism has borne the brunt of "liberal hostility" in its battles to fight for values it considers to be "fundamental pillars of a rightly ordered society".
"The vocal minority who argue that religion has no role in modern British society portray Catholic teaching on the family as prejudiced and intolerant to those pursuing alternatives," he says.
In particular, the cardinal highlights the Church's opposition to liberal laws on abortion and homosexuality, its defence of faith schools and its support for marriage.
He led the Church's unsuccessful attempt to block the controversial embryo Bill, which allows for saviour siblings and babies to be born without fathers.
The campaign raised questions over the role of religion in influencing public policy, but the cardinal argues that moves to silence the faith communities must be resisted.
"There is a current dislike of absolutes in any area of human activity, including morality," he says.
"The intolerance of liberal sceptics can be as repressive as the intolerance of religious believers. Catholics are not alone in watching with dismay as the liberal society shows signs of degenerating into the libertine society."
He blames the culture of individual rights, encouraged by the Human Rights Act, as responsible for creating a society that claims to be tolerant, but in fact denies the rights of religious groups to act according to their conscience and beliefs.
"British society champions tolerance and freedom, but that freedom is dependent on responsibility," he says.
"A simplistic belief that right or wrong is an individualistic construct denies our responsibilities to neighbour and wider society."
In the book, the cardinal says that the need for defining limits of tolerance is particularly clear in the debate over multiculturalism.
Guy Lodge, senior fellow at the IPPR and the book's co-editor, said: "Though many members of religious groups would not agree that they are subject to unfair or arbitrary discrimination because of their beliefs, there is some evidence that faith communities feel increasingly estranged from certain aspects of British culture."
Keith Porteous Wood, executive director of the National Secular Society, said: "Secularists and atheists are finding it necessary to express their views more vocally because of the increasing demands made by Christians and minority faiths. The position of bishops and the Vatican on moral issues such as abortion and contraception is at odds with the views of people in the pews and in the country as a whole. We support the right of everyone to express their religion and their views in public but we have a problem with religion having a privileged place, as it does with bishops in the House of Lords."
In the book the cardinal says: "Immigrant groups have an obligation to understand, respect and adjust to the ethos of the society they are opting to join. Our society has a corresponding obligation to encourage and help them to do so."
Earlier this year, Dr Rowan Williams, the Archbishop of Canterbury suggested it was inevitable that Islamic sharia law would be adopted in this country. [Sunday Telegraph]