Judges last month dismissed challenges against the Home Office’s policy designed to curb small boats from crossing the Channel.
But lawyers representing Asylum Aid, one of the groups that brought the legal action last year, said it hopes to appeal against the decision on the basis that the court “erred” in elements of its judgment.
Asylum Aid, which provides legal advice to asylum seekers and refugees, said it would be challenging parts of the judgment related to the safety of Rwanda for migrants.
It will also look to appeal against the judges’ ruling about access to legal support for those threatened with deportation.
Alison Pickup, director of Asylum Aid, said: “We’re extremely disappointed by the High Court’s decision.
“It’s very hard to see how it can be fair for the Home Office to decide to send hundreds, if not thousands, of asylum seekers to Rwanda without any of them having a right to argue that it’s not a safe place.
“We’re asking for permission to appeal so that we can continue to fight for fair processes and fair outcomes for people who come here seeking protection.”
Tessa Gregory, a partner at Leigh Day which represents the legal protection charity, said: “In its appeal, Asylum Aid will argue the court erred in concluding that individuals threatened with removal to Rwanda do not have to be afforded an opportunity to make representations on the Home Secretary’s conclusion that Rwanda is a safe country.
“It was on the basis of that finding the court went on to conclude that affected individuals do not need access to lawyers and that seven days is enough for them to make representations about why they shouldn’t be sent to Rwanda.
“Our client considers this judgment must be challenged and, given the weight of case law supporting our client’s position, we consider an appeal has clear prospects of success.”
In April last year, then-home secretary Priti Patel signed an agreement with Rwanda for it to receive migrants deemed by the UK to have arrived “illegally”, and therefore inadmissible under new immigration rules.
Several challenges were brought against the proposals, which were described at the time as a “world-first agreement” in a bid to deter migrants from crossing the Channel.
The first deportation flight – due to take off on June 14 – was then grounded amid a series of objections against individual removals and the policy as a whole.
However, at the High Court in London in December, senior judges rejected arguments that the plans were unlawful.
Lord Justice Lewis, sitting with Mr Justice Swift, dismissed the challenges against the policy — which has already seen the UK pay Rwanda £140 million — as a whole.
However, they did rule in favour of eight asylum seekers, finding the Government had acted wrongly in their individual cases.
Following the ruling, Home Secretary Suella Braverman said she remained “committed” to sending migrants to Rwanda as soon as possible.
The UK Government has refused to put a date on when the first flight to Kigali could take off, recognising the threat of further legal action.
Speaking at an event during this year’s Conservative Party conference in October, Ms Braverman said the legal battles in this case could go to the UK Supreme Court or European Court of Human Rights in Strasbourg, and that “unfortunately you have got to let that play out”.