Bishop of Salisbury Rt Rev Nicholas Holtam spoke after the Trussell Trust, which operates 400 foodbanks across the country, said it handed out 519,342 packages in the first half of this year.
It's now on course to hand out the highest number of food parcels in its 12-year history.
Bishop Nicholas told Premier: "We need to find a way not dealing with [struggling families] through charity, though that's a good thing, but actually finding a way of dealing with them justly in the normal processes of the state.
"Many people have seen the film 'I, Daniel Blake'. There's something happening where a group of people are being left out of society [and] don't feel as though they've got much of a stake within it."
Meanwhile the Trussell Trust is warning its staff are spending a "significant" amount of time waiting on hold during phone conversations with the Department of Work and Pensions as they try to resolve client benefits issues.
The organisation's calling for each of its branches to have a telephone hotline to a local Job Centre Plus to help ensure families aren't waiting longer than necessary for issues to be fixed.
Giving her reaction to the idea, manager of the Trussell Trust's foodbank in Hammersmith and Fulham, Daphime Aikens, told Premier's News Hour: "Anything that will reduce the stress and anxiety that our clients suffer from while they're waiting for benefit issues to be sorted will be a benefit for everyone.
"Being made to make those calls in the foodbank and people - arriving to get their food parcels - being able to leave knowing that there's an ending in sight, knowing what stage their at with their claim is fantastic."
Foodbank network director Adrian Curtis told Premier: "Everybody who has been referred to the foodbank is in a position where they're struggling to put food on the table and pay a bill, for example.
"So, for those people, to get those issues resolved as soon as possible is vitally important.
"Where those benefit advisors are able to talk directly to people in a local job centre about the problems a client is facing, many of those issues can be resolved relatively quickly."
The Trussell Trust says 44 per cent of its referrals concern a level of benefit being changed or stopped altogether in the form of a sanction, or benefit delays.
Listen to Bishop of Salisbury Rt Rev Nicholas Holtam speaking with Premier's political editor Martyn Eden:
Listen to Adrian Curtis from the Trussell Trust speaking with Premier's Alex Williams:
Listen to Daphime Aikens from Hammersmith and Fulham's Trussell Trust foodbank speaking with Premier's Hannah Tooley: