Campaigners are warning that religious freedom may be at risk as a Christian-run bakery in Northern Ireland faces a court battle over its refusal to make a cake in support of gay marriage.

The McArthur family, who own Belfast-based Ashers Baking Company, decided against fulfilling an order from LGBT activist Gareth Lee who wanted a cake decorated with the words "Support Gay Marriage".

The cake was also to be emblazoned with characters Bert and Ernie from Sesame Street locked in an embrace, along with the logo for QueerSpace – a campaign group for LGBT rights.

Though the order was originally accepted by shop staff, the management later decided to withdraw from the agreement on grounds of religious beliefs and Karen McArthur, who owns the company with her husband, Colin, phoned Lee to explain and offer a refund.

Just less than two months later, watchdog Equality Commission sent the McArthurs a letter accusing them of discrimination, and the family now face a legal battle in court.

"We are Christians and our Christianity reaches to every point of our lives, whether that's at home or in the day-to-day running of the business," Colin McArthur has said of the controversy.

"We thought that this order was at odds with our beliefs, certainly was in contradiction with what the Bible teaches. Although we have found this experience certainly unsettling and disruptive to our day-to-day business, we are certainly convinced that we have made the right decision, and we continue to take the stance that we do take."

Colin Hart of the Christian Institute, which is supporting the McArthurs, warned that the bakery's case "is a sign of things to come exactly as we predicted".

Insisting that there must be room within the law to "reasonably accommodate family-run businesses with firmly held beliefs", Hart added: "The Government repeatedly failed to listen to members of the public, lawyers, constitutional experts even its own MPs when they called for safeguards to protect those who back traditional marriage, whether at work or in business.

"All the McArthurs want is to run their bakery according to their Christian beliefs. There won't be many situations where they need to turn down an order but this is obviously one of them. No one should be forced to use their creative skills to promote a cause which goes against their consciences. Imbalanced equality laws are making it increasingly hard for people, especially Christians."

Hart went on to suggest that the law is biased against Christians. "Imagine the uproar if the Equality Commission said that an environmentally-conscious baker had to produce a cake saying 'Support fracking?' Or if they threatened a feminist bakery for refusing to print a 'Sharia for UK' cake?" he said.

"Millions of ordinary people who do not agree with gay marriage, face intimidation and the real threat of legal action from the forces of political correctness if they, out of conscience, decline to provide goods or services to campaign groups they do not agree with or support.

"It establishes a dangerous precedent about the power of the state over an individual or business to force them to go against their deeply held beliefs."

The Christian Institute is thus calling for "urgent action" from the UK government to protect religious conscience.

A spokesman for the Free Church of Scotland today labelled the McArthur's case "alarming", and joined the Institute's call in insisting that more needs to be done to promote religious liberty in the UK.

"It is alarming that Christians in the UK could be taken to court for refusing to act against their own deeply held beliefs. It would be extremely unfair to bring a legal action against the bakery, especially as Northern Ireland is a country where same-sex marriage is illegal," he said.

"A fair society is certainly not where you take people to court because they refuse to comply with your own militant agenda. If this case is successful, we will be effectively operating in a censorship police state rather than a democracy."

The spokesman also suggested that any conviction against the bakery would be "a crushing blow to civil and religious liberties, and send a loud message that personal conscience has no place in the public square".

Britain's most senior female judge, Baroness Hale, recently suggested that a "more nuanced approach" may be necessary when dealing with issues of religious liberty in court.

"I am not sure our law has found a reasonable accommodation of all these different strands," she said. "Should we be developing an explicit requirement upon providers of employment, goods and services to make reasonable accommodation for the manifestation of religious beliefs?

"If the law is going to protect freedom of religion and belief it has to accept that all religions and beliefs and none are equal. It cannot realistically inquire into the validity or importance of those beliefs, or any particular manifestation of them, as long as they are genuinely held," she added.

Watch the Christian Institute's campaign video here: