Secular groups have welcomed a Strasbourg court ruling that religious freedoms do not trump other human rights as a victory against discrimination.

Keith Porteous Wood, the executive director of the National Secular Society, described the court's decision that a British Airways check-in worker should have been allowed to wear a cross at work was only a "limited" right that needed to be balanced against other interests.

Three other UK Christians, who appealed to the European court of human rights (ECHR) claiming that their religious liberties had been infringed, lost their challenges.

Nadia Eweida, the BA check-in worker, won her appeal but Lilian Ladele, a local authority registrar who also lives in London, Shirley Chaplin, a nurse from Exeter, and Gary McFarlane, a Bristol marriage counsellor, all had their claims dismissed.

Porteous Wood said the ECHR rulings confirmed there was no need to change UK equality law because it had been found to be "fully compatible" with the European convention on human rights.

"Any attempt to [change the law] … would therefore signal a clear desire to give privileged treatment to religious believers, and would be robustly challenged," he warned.

"In the cases of the registrar who refused to conduct civil partnerships and the counsellor who wouldn't counsel gay couples – the principle of non-discrimination against gay people has been upheld.

"If they had won these cases, it would have driven a coach and horses through the equality laws. The rights of gay people to fair and equal treatment would have been kicked back by decades.

"In the case of Eweida [the British Airways check-in worker], it is a very limited victory which simply means that if employers want to prevent an employee wearing religious symbol for corporate image purposes, they must prove that their image is negatively affected by such manifestations of belief.

"In the case of Chaplin [a nurse], we are pleased that the court has acknowledged that employers are better placed than the court to decide if jewellery is a health and safety risk, and did not support the idea of blanket permission to wear religious symbols in the workplace."

John O'Doherty of the Rainbow Project, Northern Ireland's largest gay and lesbian organisation, said: "Religious belief cannot be used as a smokescreen for discrimination, and all service providers must recognise that they may not pick and choose which members of the public are worthy of accessing services.

"We hope that the organisations which insisted on bringing these claims to the European court now recognise that there is nothing to be gained by consistently making claims of widespread discrimination against Christians without evidence or merit. The law has been tested and equality has won.

"While we had always supported Nadia Eweida's right to wear her cross, as a symbol of her faith, in the workplace, we were adamant that the McFarlane and Ladele claims of discrimination must fall."

But the Archbishop of York, the Most Revd Dr John Sentamu, insisted that courts should not have any power to prevent individuals wearing religious symbols. "'Christians and those of other faiths should be free to wear the symbols of their own religion without discrimination," he said. "Christians are not obliged to wear a cross but should be free to show their love for and trust in Jesus Christ in this way if they so wish.

"In July 2012, the General Synod stated that it is the calling of Christians to order and govern their lives in accordance with the teaching of holy Scripture and to manifest their faith in public life as well as in private. This means giving expression to their beliefs in the written and spoken word, and in practical acts of service to the local community and to the nation.

"The Equality Act 2010 encourages employers to embrace diversity – including people of faith. Whether people can wear a cross or pray with someone should not be something about which courts and tribunals have to rule."

Employment lawyers accepted the clear reasoning of the judgment. Jennifer Skeoch, an employment lawyer at the law firm Taylor Wessin, said: "The judgments clarify this long-running issue: employees may have the right to manifest their religious beliefs in some ways providing this does not adversely infringe on the rights of others or jeopardise health and safety.

"On this analysis, three out of the four applicants were unsuccessful. Businesses should take note as the blurred line on individuals' rights to manifest their religious beliefs in the workplace is becoming clearer."

Claire Dawson, at the solicitors Slater & Gordon, said: "The court has recognised the right of individuals to have some accommodation made for the expression of their religious beliefs in the workplace in a way that is reasonable and does not interfere with the rights of others. This decision seeks to strike a fair balance between the right to express religious belief, and the rights of others in the workplace.

"What this decision has told us is that employers are not obliged to make those accommodations in circumstances where they may conflict with protecting the rights of others, whether that be health and safety or equality. Employers will be obliged in many cases to accommodate reasonable requests relating to uniform.

"It is important to remember that discriminating against a person purely because of their religion, as opposed to the way they wish to express certain religious beliefs, is completely prohibited by UK law. This decision does not change that."

Audrey Williams, head of discrimination law at the firm Eversheds, said: "To the relief of employers, the ECHR has substantially upheld the approach to religious discrimination law adopted by the UK courts and found no significant inconsistency between UK law and the ECHR. However, this is subject to an important caveat: that employers strike a fair balance between the respective interests of religious beliefs and requirements in the workplace."

Shami Chakrabarti, the director of the human rights group Liberty, said: "[This] judgment is an excellent result for equal treatment, religious freedom and common sense. Nadia Eweida wasn't hurting anyone and was perfectly capable of doing her job whilst wearing a small cross. She had just as much a right to express her faith as a Sikh man in a turban or a Muslim woman with a headscarf.

"British courts lost their way in her case and Strasbourg has actually acted more in keeping with our traditions of tolerance. Let's hope that some of those who threaten to pull out of the ECHR remember this case in the future. However, the court was also right to uphold judgments in other cases that employers can expect staff not to discriminate in the discharge of duties at work."

The Liberal Democrat MEP Sarah Ludford also welcomed the decision, saying: "The court has struck exactly the right balance in judging that BA's corporate image policy should not override right of BA stewardess Nadia Eweida to wear a cross whereas genuine health and safety issues in a hospital could rule out nurse Shirley Chaplin's desire to wear one.

"The insistence by registrar Lilian Ladele and Relate counsellor Gary McFarlane that their Christian consciences made them refuse to perform certain duties was unacceptable because it could result in unacceptable discrimination against gay clients."

"Employees cannot allow their personal religious beliefs to interfere with the prescribed duties of their employment and the standards of service they provide to service-users. A religious conscience does not give you a free pass to discriminate in the workplace."