The Christian owners of a hotel in Cornwall who banned a gay couple from staying have lost their final battle in the British courts to win legal support for their selective guest policy.

The supreme court unanimously dismissed an appeal by Peter and Hazelmary Bull that their right to express their religious beliefs had been breached.

The Bulls operate a policy at their hotel, stated on their online booking form, that double bedrooms are available only to "heterosexual married couples".

The case was originally brought by Martyn Hall and Steven Preddy, a gay couple, whose booking was refused in September 2008.

The supreme court judges said that although the Bulls' rights under the European convention on human rights to manifest their religion were at issue it was justifiable and proportionate to limit them in order to protect the rights of others.

Delivering judgment, the deputy president of the supreme court, Lady Hale, said: "Sexual orientation is a core component of a person's identity which requires fulfilment through relationships with others of the same orientation."

Homosexuals, she added, "were long denied the possibility of fulfilling themselves through relationships with others … This was an affront to their dignity as human beings which our law has now (some would say belatedly) recognised.

"Homosexuals can enjoy the same freedom and the same relationships as any others. But we should not under-estimate the continuing legacy of those centuries of discrimination, persecution even, which is still going on in many parts of the world."

There was no question of replacing legal oppression of one community with legal oppression of another, she maintained. "If Mr Preddy and Mr Hall ran a hotel which denied a double room to Mr and Mrs Bull, whether on the ground of their Christian beliefs or on the ground of their sexual orientation, they would find themselves in the same situation that Mr and Mrs Bull find themselves."

After the ruling, Hazelmary Bull said: "We are deeply disappointed and saddened by the outcome. We are just ordinary Christians who believe in the importance of marriage as the union of one man and one woman.

"Our B&B is not just our business, it's our home. All we have ever tried to do is live according to our own values, under our own roof.

"These beliefs are not based on hostility to anyone – we certainly bear no ill will to Steven and Martyn. Our policy is based on our sincere beliefs about marriage.

"Britain ought to be a country of freedom and tolerance, but it seems religious beliefs must play second fiddle to the new orthodoxy of political correctness.

"We appealed to the supreme court to introduce a bit more balance when dealing with competing rights of sexual orientation and religious liberty. Somehow, we have got to find a way of allowing different beliefs to coexist in our society. But the judges have sidestepped that big issue, and reinforced the notion that gay rights must trump everything else.

"What does this mean for other people in Britain who believe in traditional marriage – not just Christians, but Muslims, Jews, people of all faiths and none?"

Mike Judge, a spokesman for the Christian Institute which supported the Bulls' appeal, said: "What this case shows is that the powers of political correctness have reached all the way to the top of the judicial tree. So much so that even the supreme court dare not say anything against gay rights.

"Lady Hale effectively said gay rights are almost untouchable because of the rulings by European judges. This ruling is another slap in the face to Christians, and shows that the elite institutions are saturated with a liberal mindset which cares little about religious freedom.

"Parliament needs to reform the law to allow a more reasonable approach which balances competing rights. Otherwise, Christianity will become the belief that dare not speak its name."

But Wendy Hewitt, deputy legal director at the Equality and Human Rights Commission, welcomed the ruling. "The courts have been very clear throughout this long-running case that same-sex couples should not be subjected to discrimination when accessing services," she said.

"This is what parliament intended when it approved the 2007 sexual orientation regulations and then passed the Equality Act 2010, well aware that gay men and lesbians have long suffered discrimination when seeking to stay away from home as a couple. Each of these parties has the same right to be protected against discrimination by the other."

Phil Allen, employment partner at the law firm Weightmans, said: "Where characteristics protected by equality legislation conflict, employers, and ultimately courts, face a challenging balancing act. The judgment reinforces the message that no individual may insist on manifesting their religious beliefs, whether in a commercial or employment context, where the rights of others may be impacted."