A British Airways check-in worker's right to express her religion was unfairly restricted when she was prevented from wearing a cross at work, the European court of human rights (ECHR) has ruled.

In a landmark judgment defining the limits of religious freedom, Nadia Eweida, 60, a practising Coptic Christian, was awarded €2,000 (£1,600) in compensation by the court in Strasbourg after it ruled against the United Kingdom.

But three other Christian applicants – Lilian Ladele, a local authority registrar who also lives in London, Shirley Chaplin, 57, a nurse from Exeter, and Gary McFarlane, 51, a Bristol marriage counsellor – who also claimed they had suffered religious discrimination lost their appeals.

Secular groups welcomed the four decisions, all contained in one judgment, on the grounds that religious liberties were not allowed to trump other human rights.

In Eweida's case, the Strasbourg court did not criticise UK law but said British courts had failed to balance competing interests in the case adequately.

On the one hand was Eweida's desire to display her religious belief; on the other was the employer's wish to project a certain corporate image. "While this aim was undoubtedly legitimate," the judgment said, "the domestic courts accorded it too much weight."

In its majority judgment, the ECHR declared: "The domestic authorities failed sufficiently to protect the first applicant's right to manifest her religion, in breach of the positive obligation under article 9 [of the European convention on human rights, which guarantees freedom of thought, conscience and religion]."

The judges added: "The fact that the company was able to amend the uniform code to allow for the visible wearing of religious symbolic jewellery demonstrates that the earlier prohibition was not of crucial importance."

The prime minister, who intervened in the debate last summer by saying he might change the law, welcomed the ruling. He wrote on Twitter: "Delighted that principle of wearing religious symbols at work has been upheld - ppl shouldn't suffer discrimination due to religious beliefs."

But in Chaplin's case, which was superficially almost identical, the judges unanimously decided the British courts had resolved competing rights equitably.

Chaplin had also stressed the importance for her to be allowed to bear witness to her Christian faith by wearing a crucifix visibly around her neck at work. In her case, however, the Strasbourg judges considered the fact that hospital authorities had asked her to remove it for the protection of health and safety and to prevent infections spreading on a ward "was inherently more important". Hospital managers, the judges agreed, "were well placed to make decisions about clinical safety".

The appeals by the other two claimants, Ladele and McFarlane, were dismissed on the grounds that the disciplinary proceedings against them were justified. Ladele was disciplined by Islington council for not being prepared to conduct civil partnership ceremonies. McFarlane was dismissed from his job after indicating he might have a conscientious objection to providing sex therapy to a same-sex couple on account of his Christian faith.

Both Islington council and the charity Relate were bound by duties not to discriminate against their clients and therefore could not support staff who refused to work with homosexual couples, the court said.

After the ruling, Eweida, who lives in Twickenham, said: "I'm very pleased that after all this time the European court has specifically recognised … that I have suffered anxiety, frustration and distress. It's a vindication that Christians have a right to express their faith on par with other colleagues at work visibly and not be ashamed of their faith.

"I'm disappointed on behalf of the other three applicants but I fully support them in their asking for a referral for their [appeals] to be heard in the [ECHR's] grand chamber, and I wish them every success in the future to win."

Andrea Williams, director of the Christian Legal Centre, which supported the cases, said: "We are delighted that the cross has been recognised and indeed that Nadia has won her case. We are saddened that Shirley Chaplin lost her case."

In the cases of Ladele and McFarlane, she added, sexual rights had been given priority over religious liberty: "[The judges said] that if an employer has an equalities policy and says there should be no discrimination in any way on the grounds of sexual orientation no matter what your Christian belief is that the sexual orientation rights win."

British Airways said the airline was not a party to the legal action, which was taken against the UK government. A spokesman said: "Our own uniform policy was changed in 2007 to allow Miss Eweida and others to wear symbols of faith and she and other employees have been working under these arrangements for the last six years. Miss Eweida has worked continuously for British Airways for 13 years."

The equalities minister, Maria Miller, said: "We are delighted the principle that one can wear religious symbols at work has been upheld. People shouldn't suffer discrimination because of their religious beliefs.

"We are absolutely committed to the rights of Christians and people of all beliefs to follow their faith openly and being able to do so at work is a vital freedom."

In a dissenting judgment, two ECHR judges, Nebojsa Vucinic and Vincent de Gaetano, said Ladele's right to freedom of conscience had been infringed. They explained: "We are of the view that once a genuine and serious case of conscientious objection is established, the state is obliged to respect the individual's freedom of conscience."

They also launched a fierce verbal attack on the culture prevalent in her local authority: "In the third applicant's case, however, a combination of backstabbing by her colleagues and the blinkered political correctness of the borough of Islington (which clearly favoured 'gay rights' over fundamental human rights) eventually led to her dismissal."