It also said they have seen evidence to suggest energy companies are getting around the law, which bans them from shutting off someone's power if they're deemed to be vulnerable, by using pre-pay meters.
Energy companies are currently allowed to file for a court order to install a pre-pay meter in someone's home, if they run up debts.
Liam Purcell, from Church Action on Poverty, told Premier's News Hour: "We've been working with Ofgem and campaigning and lobbying, it's great to see that they're doing stuff on this.
"You pay more if you're on a pre-payment meter, so effectively the people who are least able to pay are being expected to pay the highest prices. It doesn't have to be that way, the market can work in ways that support people in poverty rather than exploiting them.
"People who are in rented properties often find that they're paying someone else's debts, and it's very, very difficult to get the companies to acknowledge that and correct it.
"[Also] we're always told... there's a market, there's competition. If you're on a pre-payment meter it's very difficult to switch.
"The energy companies have a requirement that they must not disconnect people who are vulnerable, where their health or their lives could be put in danger by the energy company disconnecting them.
"We've seen evidence that they're getting around that... if they install a pre-payment meter then technically when the money runs out the person's self-disconnected."
Listen to Liam Purcell speaking to Premier's Des Busteed on the News Hour: