The Trussell Trust, a Christian organisation and the country's largest foodbank operator, blamed a wait for benefit payments under the switchover to Universal Credit (UC).
Managers are reporting a 30 per cent increase in demand for their emergency food parcels in areas where UC has already come into effect, a rise higher than places where it is not yet operational (15 per cent).
Tony Graham, Director of Devolved Nations at the Trussell Trust, told Premier: "There is a six-week wait before they actually get their benefits when they go onto Universal Credit and we're asking the Government to see whether they can bring that figure down to about four weeks.
"There's an obvious way that you can bring that wait down; that would help the situation."
In response, the Government's Department for Work and Pensions said it would be "misleading" to suggest foodbank use is linked solely to one issue.
A spokesman added: "We're clear that advance payments are widely available from the start of anyone's UC claim, and urgent cases are fast-tracked so no-one should be without funds.
"We know the majority of UC claimants are confident in managing their money. Budgeting support and direct rent payments to landlords are also available to those who need them."
The Trussell Trust expects to hand out a record number of food parcels from its 428 centres this financial year - many of whom operate out of churches.
Click here to listen to Premier's John Pantry and Rosie Wright speaking with Tony Graham from the Trussell Trust: