"Our society has a corresponding obligation to encourage and help them to do so," The Telegraph quotes Murphy-O'Connor as saying further while blaming the rise of secularism as the key factor behind a British society that is liberal and is hostile to Christian morals and values.
Religious belief is viewed as "a private eccentricity" and the voice of faith groups is marginalized, he says.
Britain, the cardinal adds, is now showing 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.
In a book on multiculturalism, to be published on Monday, he 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.
The book, called Faith in the Nation, is published by the Institute for Public Policy Research (IPPR), with the backing of Prime Minister Gordon Brown.
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".
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.
Earlier this year, Dr Rowan Williams, the Archbishop of Canterbury suggested it was inevitable that Islamic sharia law would be adopted in this country. (ANI)