If they received the national living wage, the estimated value of their work would total £30 million annually, the Independent Food Aid Network (Ifan) found.
The Trussell Trust, a Christian charity and the largest operator of food banks in the nation, paid tribute to the "tireless" people of its unpaid workers but said they cannot replace the welfare system.
Samantha Stapley from the organisation said: "Issues with benefit payments remain the main reason why people need a food bank parcel, and with issues caused by Universal Credit increasingly reported by food banks as a concern, we urge the Government to take steps to make sure people don't face going hungry."
More than 700 food banks now operate independently across the country, in addition to the 1,235 Trussell Trust-managed centres.
Ifan accused the Government of "relying" on food banks and it urged ministers to accept their "responsibilities" for Britain's "hunger crisis".
Professor Jon May from Ifan said: "Even as the Government plans £12 billion in cuts to social security benefits by 2019/20, some of our largest companies continue to avoid paying their fair share in tax.
"Though we already pay £11 billion a year to subsidise a low-wage economy because employers are not paying people enough to live on, volunteers up and down the country are providing a further £30 million a year in 'free' labour to ensure that our fellow citizens in low paid work, on zero hour contracts, or relying on a broken benefits system have enough to eat.
"Whilst we must continue to support those in need, we must also advocate for fundamental change."
The Government said it was "misleading" to link food bank reliance to any one cause, arguing it's a "complex" issue.
A Department for Work and Pensions spokesman said: "We continue to spend around £90 billion a year supporting people, including those who are out of work or on a low income.
"Work is the best means of providing people with financial security, and with our welfare reforms people are moving into employment faster and staying there longer than under the old system."