Researchers at Liverpool University said the patients had all received one dose of the vaccine at least three weeks before they were admitted.
They said the patients were largely frail and elderly, while the number of people who were hospitalised represented only around 1 per cent of the 52,000 people involved in the research.
The report warns: “Elderly and vulnerable people who had been shielding, may have inadvertently been exposed and infected either through the end-to-end process of vaccination, or shortly after vaccination through behavioural changes where they wrongly assume they are immune.”
The study found a total of 526 people were admitted to hospital and 113 people died in what the research team called “vaccine failures”.
But they noted the amount of failures were not surprising based on the results at trials.
Colin Semple, professor of outbreak medicine at Liverpool University and one of the study’s authors, told the Times: “People should not be surprised about some vaccine failure. It is what was predicted. It does result in tragedy.
“We are all talking about the statistics, but if it is your granny it is a tragedy for your family.”
The findings were published by the UK Scientific Advisory Group for Emergencies.
The authors pointed out that during the period covered by the study, December 8 to March 10, 2021, vaccinations were heavily focused on older people.
The study’s findings come as the government prepares to scrap controversial rules banning care home residents from leaving their accommodation.
From Tuesday residents will be able to leave care homes for “low risk" visits without having to self-isolate for 14 days on their return.
The Department of Health and Social Care (DHSC) are relaxing the rules after being threatened with legal action by the charity John’s Campaign.
Campaigners said strict rules encouraged care homes to act unlawfully by "falsely imprisoning" residents, with family members calling it "barbaric".
Under the changes, residents on visits out must be accompanied by either a member of staff or one of their two nominated visitors, and follow social distancing throughout.
They cannot meet in groups or go indoors - except for the use of toilets - and public transport should be avoided where possible.
It is understood a resident would be able to eat outside at a restaurant or cafe with their care worker or nominated visitor if they agree it with the care home in advance.
Residents will also be able to vote in person in the upcoming local elections without having to self-isolate for 14 days afterwards.
The DHSC is expected to review the self-isolation requirement for more visits when it reaches the next stage of the Government’s road map on May 17.
New data shows that 95 per cent of elderly care home residents have received one vaccine dose and 71 per cent have received two.
Prime Minister Boris Johnson said: "We know how challenging this time has been for care home residents, so I am pleased that they can now leave their homes to reunite with their loved ones outdoors.
"With the data continuing to head in the right direction and as restrictions ease, it is my priority to keep increasing visits for residents in the coming weeks in a safe and controlled way."