The report indicates nearly a quarter of men and a sixth of women over the age of 55 who think they hear well actually have a hearing loss.
And less than a third of all adults with a hearing loss use a hearing aid.
The charity Action on Hearing Loss said it took most people a decade to seek help.
It is the first time the annual health survey, conducted by NatCen Social Research, has compared people's perceptions about their hearing with the results of actual tests.
Dr Jennifer Mindell, from UCL and one of the authors of the section on hearing, said the findings were worrying.
She told the BBC: "Whether people are in denial or just unaware of what they can't hear we don't know."
She said about half of the people who had said they had "great difficulty" hearing still did not use a hearing aid.
Dr Mindell said: "People think it's a normal part of ageing, and some don't want a hearing aid as they feel there's a stigma attached in a way that people don't with glasses."
Untreated hearing loss can lead to social exclusion due to the restrictive effect on conversation.
Dr Mindell said it was a "cause for concern" and there was a link between untreated hearing loss and poor mental health.
The report suggests:
Gemma Twitchen, an audiologist with the charity Action on Hearing Loss, said: "Reluctance to acknowledge hearing difficulties is far more common than we might think - on average it takes people 10 years to seek help for hearing loss.
"Early diagnosis is key, and hearing aids are vital in ensuring people can continue to communicate better with friends and family.
"We would urge anyone that is concerned about their hearing to take our free hearing check."
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John Rosa, president of the Citadel college, said he found the images "offensive and disturbing".
The cadets wore the hoods and all-white clothing as part of a Christmas skit.
The Citadel Minority Alumni Association shared one of the photos on its Facebook page, calling it a "disgrace".
In it, seven cadets are seen wearing the pillowcases. Another cadet is also seen with them.
Founded in the aftermath of the US Civil War, the KKK is notorious for targeting black people with lynchings and cross burnings.
"These images are not consistent with our core values of honour, duty and respect," said Mr Rosa in a statement. An investigation is underway.
The alumni group said it was pleased at the South Carolina college's response but added more needed to be done "to address the culture that continues to house recurring prejudices against minority cadets".
A previous incident in 1986 saw five cadets dressed in KKK robes drag a burning cross to a black cadet's room, the Washington Post reported.
Around two million people who need a hearing aid do not even realise they have problems, the annual health survey for England suggests.
[NEXT_CONCEPT]
A top US military college says it has suspended eight cadets seen in photos wearing pillowcases resembling hoods worn by the white supremacist Ku Klux Klan.