The Bureau of Investigative Journalism spoke to ten GP surgeries in Luton and found that none were willing to register an undocumented migrant.
Nine surgeries gave an outright refusal, while a tenth stated they were unsure if they could register the patient.
Being refused registration removes the option of being vaccinated by a surgery, as well as the option to book a Covid-19 vaccine appointment via the NHS website or 119 helpline.
However, unregistered patients can still access Covid-19 vaccines at walk-in centres and drop-in clinics set up around Luton, without the need for a NHS number.
Of the 210 UK surgeries The Bureau of Investigative Journalism (BIF) spoke to, less than a quarter (24%) said they would definitely register an undocumented patient.
A BIF spokesman said: "Luton was the area where we encountered the greatest barriers, with none of the surgeries contacted agreeing to register our dummy patient.
"Our callers were often given incorrect information. For example, one Luton surgery told us, 'she won't be able to get vaccinated until she's got an NHS number'."
Evidence suggests ethnic minorities are more likely to die from Covid-19. A study by Public Health England found that deaths in the early months of the pandemic were more than three-times higher for UK residents born in Africa, the Caribbean, South East Asia, and the Middle East.
According to Anna Miller, head of policy at Doctors of the World, migrants could lose ID as a result of difficult routes taken to enter the UK, or their passports could reveal that their residency visa has expired, making them hesitant to show it to people.
Meanwhile, since undocumented migrants are banned from having UK bank accounts or renting, they may be unable to produce bank statements or tenancy agreements.
NHS England guidance states on its website: “Anyone in England can register with a GP surgery. It’s free to register. You do not need proof of address or immigration status, ID or an NHS number”.
A spokesman for Bedfordshire, Luton and Milton Keynes CCG said: “All adults in Luton, regardless of their immigration status or registration with a GP practice, are able to have their Covid vaccine at one of our large vaccination centres or drop-in clinics.
“We are working hard to make accessing the vaccine as convenient as possible for everyone, by taking vaccination buses into town centres and community settings, and would urge everyone to have their jab as soon as they can.”
The CCG added that all local GP practices are being reminded of how undocumented migrants, and other groups who may not have an NHS number, can access healthcare and the Covid vaccine.