The plans to send asylum seekers from the UK to Rwanda are part of the new refugee agreement concluded between the countries.
The idea is that the asylum process will be handled there, while the UK will bear the cost.
The scheme has previously endured harsh criticism from, among others, human rights organizations.
For example, people who in many cases risked their lives to go to Europe to seek asylum are sent to another country that does not have the same freedom of expression and rights that they have felt the need for.
The plane was canceled
The relocations have been repeatedly delayed after the agreement between the countries was appealed.
But after Britain's highest court gave the go-ahead on Monday, a first transport was planned on Tuesday night, writes the BBC.
Up to seven asylum seekers were supposed to be removed by plane, but at the last minute new information came from the British government.
The planned departure was canceled after the European Court of Justice stopped the relocation decisions in several of the cases.
Exactly what decisions the European Court of Justice has made is still unclear, but in a statement before the departure, the court announced that an "urgent interim measure" had been taken in the case of an Iraqi man who was to be relocated by plane.
"The court takes such measures only on exceptional grounds, when the applicant is otherwise faced with a real risk of irreversible damage," the statement reads.