The Catholic Bishops Conference of England and Wales said that the passing of same-sex marriage into law "marks a watershed in English law and heralds a profound social change."
Archbishop of Westminster the Most Rev Vincent Nichols and the Archbishop of Southwark Peter Smith said in a statement: "The new Act breaks the existing legal links between the institution of marriage and sexual complementarity.
"With this new legislation, marriage has now become an institution in which openness to children, and with it the responsibility on fathers and mothers to remain together to care for children born into their family unit, are no longer central.
"That is why we were opposed to this legislation on principle."
More top news
Cancer battler Bradley Lowery is back in hospital with "horrendous pain" as doctors fear the disease is progressing.
Children's health services are being put at risk by a serious shortage of paediatricians and concerns over Brexit, a report warns.
A veteran has been accused of tying her therapy dog to a tree and shooting it dead while her soldier boyfriend filmed it.