Economy 7 is an electricity-only tariff where you pay different rates depending on the time you use your energy. You need a special meter which shows a day and night rate.
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You CAN usually still save money by switching if you have Economy 7. But these tariffs are only really worth it if you have storage heaters or work shifts, or can use appliances on timers. See Is Economy 7 worth it? for more info.

Economy 10, Economy 15 and Eco 20:20 are similar types of tariff, but with different low-rate hours. Unfortunately it's difficult to compare these tariffs, so to switch you'll need to ring around suppliers to find the best quote.