Ofgem has published new guidance for tenants making it clear that they have the right to choose their own supplier if they are directly responsible for paying the bill.
The energy regulator's 2013 customer engagement survey found that 77% of bill payers living in rented accommodation have never switched supplier, costing them an average of £190.
Ofgem said it was concerned that many tenants may not know their rights, or the potential gains that come from switching suppliers.
It said: "Today's guidance for tenants is intended to help bust myths and break down information barriers that might be a contributing factor to the low switching rate."
The guidance also suggests tenants look for any clauses in the agreement relating to energy suppliers, inform the landlord or letting agent after switching and take meter readings when moving into and out of a property.
Ofgem spokesman Philip Cullum said: "At a time when nine million British households are renting and budgets are tight, it is important that consumers are clear about where they stand when choosing and switching their energy supplier.
Ann Robinson, director of consumer policy at price comparison website uSwitch, said: "With Britain's army of renters growing, and winter fast approaching, this guidance from Ofgem is right on cue and very welcome.
"It's imperative that any myths around tenants switching their energy suppliers are busted immediately - our own research shows that less than a third of private renters are aware that they can switch energy suppliers, subject to their rental contract.
"Being a tenant does not mean relinquishing the right to control household bills, nor should it mean you miss out on the savings to be made by switching. While landlords can require in the rental contract that the tenant has to ask their permission, they cannot restrict them from moving to another supplier.
Carolyn Uphill, chairwoman of the National Landlords Association, said: "As energy prices rise, it's essential that bill payers get the best value for money and when looking to rent a new property, tenants should consider the total cost of living in the property, including the bills, rather than the rent alone.
"We encourage tenants to shop around for the best deal and switch to a new, more competitively priced supplier. However, as a courtesy, we advise tenants to inform their landlord if they plan to change energy supplier and ask permission to add new wiring or equipment if this is required."
Energy Secretary Ed Davey said: " I'm very aware of the pressure on household budgets, not least with energy bills.
"It's simply shocking that only 23% of consumers in rented accommodation have ever switched their gas or electricity supplier. We know that switching can save people significant amounts of money. There is no reason tenants in rented accommodation should be left out in the cold this winter.
"People in rented accommodation that are responsible for paying their energy bill have the right to decide who they get their energy from. However, a lot of these people simply don't know their rights. That's why I welcome Ofgem's guidance for tenants. Landlords and letting agents should also make sure they are not preventing their tenants from switching."