Action for Children said the nation "can't go back" to the scenes of desperation described by the Victorian author.
The comments come after the charity said it has been regularly sending families to food and clothes banks for the first time since the 1940s.
Action for Children spokesman Jacob Tas said a "staggering" number of its centres were showing families where they could obtain emergency supplies.
Some 62%\ of the charity's 220 children's centres said they are regularly signposting families in need to food banks, according to its annual report, The Red Book.
And 21% of managers of the charity's intensive family support services are signposting those in need to clothes banks, said the report released earlier this year.
Mr Tas said: "It's really horrible for those families who are basically already at the bottom of the food chain that they have to go to go to food banks to get their food.
"Some families now have to make a choice between either paying the rent, paying for heating or paying for food. We are talking about children that are cold at home and are hungry.
"We have a two-tier society where people are struggling to feed and clothe themselves.
"We can't go back to the times of Charles Dickens where at Christmastime we are handing out food and clothes."
He said that there are a number of contributing factors to the rise in people seeking help for basic necessities including the economy, unemployment, changes to the benefits system and cuts to services.