Both Syrian and Afghan nationals are understood to be among those notified by the government on Tuesday of their impending deportation to the Central African country, following a hugely controversial deal struck between the two states last month.
"The plan to send refugees to Rwanda is cruel and out of step with public opinion," Freedom from Torture, a UK-based NGO, wrote on Twitter. "People seeking safety deserve so much better than this government's cruel policies.
"It is not a done deal - that's why we have to keep fighting to stop it."
Freedom from Torture is one of a group of civil society organizations, including Detention Action, that have launched legal challenges to the Home Office's plans. They have appealed for funding to support these efforts.
In a statement on Tuesday, the Home Office confirmed it had issued formal removal notices "to those who are set to go to Rwanda, where they will be able to rebuild their lives in safety.”
Zoe Gardner, head of policy and advocacy at the Joint Council for the Welfare of Immigrants (JCWI), reported that 15 Syrians had been told they will be sent to Rwanda in two weeks.
"We know that our country is better than this. We shouldn't leave the floor to retrograde rubbish," Gardener tweeted on Wednesday, calling on people to "speak up for humanity, justice and generosity".
The campaign group Protect Civilians says it has heard from Afghans, Egyptians, Kurds and Chadians who have been told they too will be "offshored".
Syria, Afghanistan and Chad have been racked by armed conflict, instability and mass displacement in recent years. Egypt is an authoritarian dictatorship and Kurds from Kurdish areas of Iraq, Iran and Turkey are acutely vulnerable to political persecution.
The UK's plan to send "illegal migrants" to Rwanda for their asylum claims to be processed was announced in April, and sparked outrage in the UK. An online survey by The Independent found that some 86 per cent of the British public opposed the move.
Opposition parties inside the UK have also criticised the Conservative government's plan. "The Rwanda scheme isn’t about deterring the criminal gangs or small boat crossings, it’s about chasing headlines regardless of reality," said Labour shadow home secretary Yvette Cooper.
"This is a completely unworkable, extortionately expensive, and deeply un-British policy. There is no proper process for identifying people who have been trafficked or tortured."
Campaigners have raised the alarm about the conditions, access to legal advice and mental health of those deported to Rwanda, which itself is a refugee-producing country. In 1994, Rwanda saw a brutal genocide in which up to a million people were killed in political and ethnic violence.
In a statement, UK Home Secretary Priti Patel said: “Our world-leading partnership with Rwanda is a key part of our strategy to overhaul the broken asylum system and break the evil people-smugglers’ business model.
“Today’s announcement is another critical step towards delivering that partnership and, while we know attempts will now be made to frustrate the process and delay removals, I will not be deterred."
More than 4,850 people have come to the UK since the Rwanda plans were unveiled: more than two and half times the number that crossed in the same period last year.