The federation claims that those on a pre-pay meter pay on average £39 more a year for their gas when compared with those on a quarterly bill.
Federation chief executive David Orr said: "The big energy companies have every right to install prepay meters in people's homes if they fail to pay their bills.
"But it's totally unacceptable for them to stick the boot into hard up families by switching them onto their very highest gas tariffs."
Meanwhile, energy regulator Ofgem has been called in front of parliament to explain its position on controversial backdated pre-pay bills.
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