The two bodies said that Westminster should ensure that electricity suppliers are obliged to provide and promote social tariffs to low-income households.
Commenting on the issue, NCC acting chief executive Philip Cullum said: "There needs to be a more consistent and effective set of social tariffs, making sure that vulnerable people are shielded from the worst effects of rising energy prices.
"Energy companies should take responsibility for this - but this week's Energy Bill provides the perfect opportunity to ensure that government is able to act if the industry fails to do so."
The NCC was established to represent consumers on a number of issues with service providers, businesses and regulators within a number of sectors.
Click here to run an energy price comparison, and see if you could be paying less for your gas and electricity.