Acorn proposed that regulators, Congress and lenders make changes to improve access to mortgages.
Matthew Reed, chief executive of the Children's Society, said families were being driven into the hands of lenders by changes to the government's social fund.
His comments come amid increasing concern that, in addition to pressing for essential changes to the Greek economy, international lenders should step up efforts aimed at reversing economic stagnation.
He has criticised government changes to welfare and targeted payday lenders, saying that he wanted to "compete Wonga out of existence", although it was later pointed out that at the time the church was an investor in Wonga.
Talks with lenders concerning changes to its loan facilities were ongoing, it said.
But as a result of the new powers it is asking for - which could be legislated for by May - the Bank will now be able to direct lenders to make changes to their lending policies.
Some lenders are already making changes to their borrowing terms.
Other lenders have been making changes to criteria, with Barclays increasing the rent needed to cover repayments to 135% in December.
Under the pressure of the financial crisis, Greece is being pressed by Germany and its international lenders to make fundamental changes to its economic system in exchange for the money it needs to avoid bankruptcy.
In exchange for the bailout money that Greece needs by March to avoid what could be a catastrophic default, the country's foreign lenders have demanded radical changes to make the state more efficient and bring in more tax revenue.
The financial challenges facing foreclosure-prevention programs come amid a debate in Washington over the effectiveness of the Obama administration's $30 billion Home Affordable Modification Program, which gives lenders incentives to make changes to borrowers' mortgages.
