A survey of over 2,000 adults by the Fair Tax Mark organisation also found that a similar number preferred to work for a company that can prove its tax payments are fair.
Most of those polled said they would trust a business if it was awarded a fair tax mark.
Emily Kenway, director of the Fair Tax Mark, said: "Hard-working people have borne the brunt of austerity measures at the same time as some multimillion-pound businesses have been avoiding paying their fair share of corporation tax.
"There is a crisis in the NHS, local libraries are closing and the social care system is on the brink of collapse.
"Businesses failing to contribute to the public purse are depriving communities across the UK of vital public services."
The organisation, launched in 2014 to assess corporation tax practices, launched a national map of businesses which have been awarded the accreditation - www.fairtaxmap.com.
Firms including the Co-op, SSE and Lush are among those that have been given a fair tax mark.