The government's "vaccine amnesty" has been criticised for not giving enough assurance to those who are too scared to access healthcare in the UK.
The Home Office has promised no action will be taken against people in the UK illegally if they register with a GP to be vaccinated.
It is part of a government effort to get as many people as possible vaccinated against the virus, which has already caused the deaths of more than 112,000 people in the UK.
But the Joint Council for the Welfare of Immigrants has said the government must do more if it wants to reassure this vulnerable group that they will be safe if they come forward.
The organisation cited a policy of data being shared between the NHS and the Home Office and the NHS charging scheme for those who are undocumented.
Chief executive Satbir Singh said: "We welcome the fact that the government is finally making an effort to tell some of the most marginalised and at-risk people in our communities that they should come forward for the COVID-19 vaccine.
"Everyone has always been able to go to a GP, regardless of their immigration status, so this is not a new policy.
"But our research reveals that nearly half of those surveyed would still be scared to access healthcare for fear of being charged or having their personal data shared with the Home Office, which could put them at risk of immigration detention or deportation.
"The government has a very poor record in building trust with migrant, refugee and BAME [black, Asian, and minority ethnic] communities. Today's move to reassure them is not enough.
"As long as the Hostile Environment policies which underpin rules around migrants using the NHS remain in place, people will still be fearful. For the sake of everyone's health, the Hostile Environment must be immediately scrapped."
The research is a survey of 310 people which found that 43% of migrants would be scared to access healthcare for fear of being charged or having their data shared with the Home Office.
Even among those who have refugee status and are, therefore, here legally, 56% would be scared to access healthcare because of the data-sharing agreement, pointing to very low trust among this vulnerable group, despite their documented status.
Many migrants who have visas are also bound by a condition known as having "no recourse to public funds" and, even though this still allows them to access free NHS care, 58% in this situation are too scared to do this, according to the research.
Bella Sankey, director of charity Detention Action, added: "It is essential for all our health that everyone is able to access vaccines easily and without fear of punishment.
"But this will only work if the Home Office immediately legislates to end all data sharing with doctors, hospitals and healthcare providers. Without this guarantee, mistrust will prevent vaccine uptake, which will harm us all."
A government spokesman said: "Coronavirus vaccines will be offered to everyone living in the UK free of charge, regardless of immigration status.
"Those registered with a GP are being contacted at the earliest opportunity and we are working closely with partners and external organisations to contact those who are not registered with a GP to ensure they are also offered the vaccine."
More than 12 million people in the UK have received their first dose of a coronavirus vaccine and the government has promised to vaccinate all those aged 50 and over, as well as younger adults in an at-risk group, by May.