Christians have vowed to continue speaking up for the historic definition of marriage after the same-sex marriage Bill was given Royal Assent on Wednesday.

Royal Assent from the Queen was the final formality in the Bill's passage through Parliament after the House of Lords approved it earlier in the week.

The first same-sex wedding ceremonies are now expected to take place in summer 2014.

In a statement, the head of the Roman Catholic Church in England and Wales, Archbishop Vincent Nichols, said the new law "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," he said.

The Archbishop welcomed the amendment to the Public Order Act making it clear that discussion or criticism of marriage "which concerns the sex of the parties to the marriage shall not be taken of itself to be threatening or intended to stir up hatred".

This gives some protection from criminal sanction to individuals when discussing or expressing disagreement with same-sex marriage.

However the Archbishop expressed particular concern about the lack of effective protection for churches that decide not to opt-in to conducting same-sex marriages, and for schools with a religious character that continue to teach in accordance with their religious tenets.

"Given the potential risk that future guidance given by a Secretary of State for education regarding sex and relationships education could now conflict with Church teaching on marriage, we were disappointed that an amendment to provide this clarity was not accepted," he said.

The Archbishop continued: "The legal and political traditions of this country are founded on a firm conviction concerning the rights of people to hold and express their beliefs and views, at the same time as respecting those who differ from them.

"It is important, at this moment in which deeply held and irreconcilable views of marriage have been contested, to affirm and strengthen this tradition."

Christian Concern said the passing of gay marriage into law was a "very sad moment for our nation" and also a "cause for lament".

"It marks a very clear departure from God's good pattern for human flourishing," the advocacy group said.

"As God's people we should also repent for where we have failed to stand for and believe in God's truth.

"But we know that there is hope both for us and for our nation in the Gospel. That's why we will continue to speak of Jesus Christ in public life and encourage you to do the same."

Christian Concern said it expected more legal challenges to be brought against Christians who follow their beliefs.

With the passing of gay marriage into law, the Evangelical Alliance said it was now the "task of the Church to model marriage to a society that has forgotten what it is".

"The state's new view of marriage means it is no longer a lifelong union between a man and a woman for the procreation of children and the foundation of family life. Now it has been changed and effectively privatised to privilege adult choice," it said.

"The changes have stripped husband and wife of their obvious meaning and marginalised adultery and consummation. Marriage is now a fluid, gender-neutral institution defined by consumer demands and political expediency and it is likely that pressure for further changes to it will follow."

The EA's director of advocacy Dr Dave Landrum encouraged Christians to have the confidence to speak and teach the truth with grace and love.

"For Christians it is important to distinguish between fact and fiction: although the law has changed, real marriage is and will always be exclusively a lifelong union between a man and woman. We can acknowledge the fact the legal definition has changed but we should also understand that we do not need to approve of the legal fiction created," he said.

"In the knowledge that God is not fazed by this, we should have confidence to speak and teach the truth with grace and love. And as we help each other to sustain marriage as a covenant before God through which two become one, I hope we will be taking valuable opportunities to witness to the good news of Jesus Christ."