Vaccine access for migrants is improving around the world and outreach efforts in Britain are an example of good practice, the Red Cross says.
Low uptake among minority groups has long been a concern for experts as countries race to shield their populations against Covid-19.
But a report by the Red Cross said that although there were still "serious obstacles," Europe was expanding access to the shots and refugees were being widely included in the Middle East.
It highlighted efforts by its British arm to get the vaccine to vulnerable groups such as recent refugees and people going through the asylum process.
The British Red Cross has distributed materials in eight languages and helped people to register with doctors to gain access to vaccines.
Further efforts included persuading people in homeless shelters to take the shot.
However, there was still some concern among migrants that their details would be forwarded to immigration authorities.
The UK government says there are no immigration checks for people being tested or vaccinated against Covid-19.
The same is true in other countries such as France, Belgium and Australia, which have said that vaccines are available to all.
“While many governments did not initially include migrants in their national responses at the outset of the pandemic, the situation is improving and positive policy shifts are increasing,” the Red Cross report said.
“It is important to continue to do better for the safety and protection of everyone.”
The report said there was still much work to do, with informal barriers remaining even after governments committed to including migrants.
Half of charity workers surveyed in a Red Cross study said migrants had raised concerns about arrest or deportation.
Fears have been raised over misinformation, including in the UK, where myths have spread that migrants are being used as guinea pigs for the vaccine.
Vaccine hesitancy “could become the primary obstacle to global immunity,” the report said.
The UK’s former health secretary Matt Hancock last month praised British Muslims for acting as “trusted voices” to ensure vaccine uptake.
Elsewhere, migrants had difficulty booking vaccinations because of missing documents or language difficulties.
Language problems were cited by the Red Cross as an issue in Turkey, where aid workers said many migrants did not know where to apply.
In Italy, booking websites in many regions required a social security number which was not available to some migrants.
Greece last month started distributing vaccines to migrant camps, including on the islands of Lesbos, Chios and Samos, after criticism that refugees were being left out.
Wealthy nations also face pressure to help global uptake by donating more vaccines to developing countries.
G20 leaders were this week urged to speed up the supply of vaccines to Africa to help close the gap between richer and poorer nations.
“To end the pandemic and drive recovery, it is urgent to break down all barriers and put in place measures that ensure access to Covid-19 vaccines for all,” said Francesco Rocca, the president of Red Cross umbrella group IFRC.
“Ensuring everyone has access to Covid-19 vaccines is not just the right thing to do from a humanitarian perspective,” he said. “It is also the smart thing to do from a health and socio-economic standpoint.”