The Christian food bank charity's warning comes as the Department for Work and Pensions finalises its plans for the next stage of Universal Credit to take to Parliament later this month.
The charity claims the next stage will further increase food bank use.
Emma Revie, chief executive of The Trussell Trust, explained: "We created our benefits system in this country to free people from poverty, not lock them into it.
"As we look at the current plans for the next stage of Universal Credit, we're really worried that our network of food banks could see a big increase in people needing help.
"Leaving three million people to wait at least five weeks for a first payment - especially when we have already decided they need support through our old benefits or tax credits system - is just not good enough."
The Trussell Trust recommends the Government moves people onto Universal Credit - rather than leaving people to make their own claim - to ensure there is no gap between old and new benefits payments.
The report also outlines a number of other proposals including expanding Universal support.
"Now is the time for our Government to take responsibility for moving people currently on the old system over, and to ensure no one faces a gap in payments when that moves happens," Revie added.
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