Barnardo's Scotland and NSPCC Scotland have also warned that Scottish Government early intervention policies, including the flagship Getting It Right for Every Child strategy, are being undermined as those working with children have to concentrate on families in the most crisis.
Although the prioritisation of early intervention has cross-party support, a report on the work of Barnardo's Scotland services found such schemes were unable to function effectively due to the number of families presenting in a state of crisis.
The report says the cumulative effect of factors such as benefit sanctions, benefit delays and price rises in basic commodities such as food and energy is tipping more families into crisis and aggravating pre-existing difficulties such as mental health problems, substance misuse and relationship breakdown.
Many of those running schemes to help children are finding they need to step in to provide basic needs such as food, clothing or help to find stable housing before they can begin to work intensively to support families.
The NSPCC, which runs Childline in Scotland, worked with Barnardo's Scotland to research the impact of austerity measures on 14 Intensive Family Support Services run in 14 Scottish local authority areas.
One service reported a 53 per cent increase in families recorded as facing three or more issues such as homelessness, poverty, debt, domestic violence and alcohol or drug misuse.
In one Scottish city a service reported that 60 per cent of new service users already had children on the child protection register.
The vast increase in sanctions for failure to abide by Jobcentre rules is having a major impact, the charities report.
Martin Crewe, director of Barnardo's Scotland, said: "It often appears as if those putting in place welfare reforms have no concept of how poor people are to start with. Even without sanctions, benefits are not keeping pace with rising costs such as food and fuel. Even if people are getting what they are entitled to, it is not enough."
Susan Galloway, senior policy researcher for NSPCC Scotland, added that is was not uncommon for children to lack basics such as a toothbrush, pyjamas or sheets on their bed.
The charities are calling for a new approach, claiming that while the Christie Commission on public services recommended more early intervention and this has wide political support, the policy is failing.
Mr Crewe added: "We have to start thinking about this differently. If we carry on, more and more families will end up slipping through the net."
The Department for Work and Pensions says the proportion of benefits processed on time is at 92 per cent, up six percentage points from 2010. A spokesman said: "This Government has taken action to help Britain's hard-working people be more financially secure through our tax and benefit changes.
"Our welfare reforms will further improve the lives of some of the poorest families in our communities, with Universal Credit making three million households better off and lifting up to 250,000 children out of poverty. We continue to ensure there is a safety net in place, spending £94 billion a year on working-age benefits to support millions of people who are on low incomes or unemployed."