Campaigners failed in their High Court bid to halt the removal which is planned for Tuesday.
A flight to take asylum seekers from the UK to Rwanda next Tuesday has been allowed to go ahead by the High Court.
Campaigners failed in their legal bid to halt the removal, but the case will be heard by the Court of Appeal on Monday.
Under the policy, those entering the UK illegally will be flown to Rwanda to apply for asylum there.
About 31 people have been told they may be on the first flight to the east African nation.
The government aims to discourage people crossing the English Channel to seek asylum by making it clear many cases will now be dealt with by Rwanda.
There will be a full judicial review of the policy before the end of July, the court heard.
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