The Home Secretary has been ordered by the Court of Appeal to "rapidly" reconsider whether refugees living on a British military base in Cyprus can enter the UK.
Six families - originally from Iraq, Sudan, Ethiopia and Syria - were among 75 individuals rescued in October 1998 from a Lebanese fishing boat bound for Italy.
It was abandoned by its smuggler crew after the engine failed.
Since then the families have mostly lived in former forces' accommodation known as Richmond Village in the Dhekelia Sovereign Base Areas (SBA).
Lawyers Leigh Day say they have been trapped in "a legal limbo" for the last 18 years, living in wholly unacceptable conditions, after the government refused to accept that the 1951 Refugee Convention applied to their case.
They were refused entry to the UK by Theresa May, the-then home secretary, in November 2014 on the grounds that they had no strong ties with Britain and could be resettled in Cyprus.
Her decision was overturned by High Court judge Mr Justice Foskett, who ruled Mrs May had failed to consider all the relevant circumstances.
The judge found that although the Refugee Convention did not apply as a matter of public international law, the UK authorities were required by policy decisions they had taken to act "within the spirit" of the convention.
Three appeal court judges - Lord Justice Jackson, Lord Justice Briggs and Lord Justice Irwin - went further than the single judge and agreed in a ruling on Thursday that the convention applied directly.
They declared that current Home Secretary Amber Rudd must take a fresh decision in the light of that finding.
In the lead judgment, Lord Justice Irwin ruled:
"The secretary of state must take the decision once more but on the basis that the Refugee Convention applies directly and the UK owes direct obligations to the claimants by operation of public international law."
The judge highlighted the "enormous delay" which had affected the families and said it was common ground that "their present conditions are quite unacceptable".
He added: "I would regard it as unreasonable and a failure of the obligations to the refugees if resettlement was not achieved rapidly".
Tag Bashir, the lead claimant, said:
"For the last 18 years, the UK Government has sought to ignore us and has left us stranded on the SBA living in awful conditions.
"All we have ever wanted is an opportunity to work and make a future for our children."
"We hope that the Home Secretary will now allow us entry to the UK. We will keep fighting until she does."
Tessa Gregory, a partner from the human rights team at Leigh Day, said: "Our clients have been in legal limbo for 18 years living in wholly unacceptable conditions on a British military base.
"They have suffered enough. Now is the time for the government to show compassion and a 'strong and stable' resolve to address this situation, which has festered for far too long."
It is understood the Home Office is considering the implications of the ruling and whether to appeal to the Supreme Court.