The schemes which are known as Local Welfare Assistance, aim to provide food, fuel and furniture to people in crisis.
However, the report, Not Making Ends Meet, from The Children's Society and the Church of England found that increasing numbers of destitute people are turning instead to food banks and other voluntary agencies for help.
The Children's Society chief executive Matthew Reed said in a statement: "Families in need of financial crisis support are often experiencing one of the hardest times of their life, such as fleeing domestic violence or experiencing a serious mental or physical health problem.
"It's vital that when they need help to buy food or nappies, put money on the electricity meter or replace a broken fridge that they can access this help quickly and easily. Instead, families who are in desperate need may find there is nowhere to turn.
"Local charities are having to step in to provide the safety net that the government and councils used to, relying on donations and volunteers to do so.
"Sadly with more and more people facing crisis, particularly as Universal Credit rollout continues apace, it's becoming increasingly urgent for local crisis support to be coordinated and more consistent so that vulnerable people don't fall through the gaps."
The report concluded that a lack of publicity, bureaucratic hurdles, and restrictive eligibility criteria appear to be deterring people from applying to Local Welfare Assistance schemes.
Rt Rev Paul Butler, Bishop of Durham said "we have a moral duty to care for people at the hardest times of their lives".
He went on to say: "Voluntary and community organisations show compassion as they support individuals and families in crisis and attempt to make up for current shortcomings in state support.
"But all too often, the support is fragmented, and the experience is bewildering to those seeking help, who frequently find themselves in a cycle of repeated crisis.
"That is why strong leadership from local authorities is desperately needed, as well as a proper debate on how to fulfil the original vision for local welfare reform. We need holistic, joined-up support that meets people's underlying needs, as well as responding to an immediate financial crisis."
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