Here in the U.S. the devices are generically called Green Plugs, although most of them are white in color.
They do work, but with several cautions. Here, our standard household electrical current is 120 volts. However, older appliances, such as yours are designed to run on 10% overage or underage on the voltage (or the equivalent in the U.K., probably 220v). This means that the voltage delivered to your house can be as much as 20%variance from the optimum. The "Green Plug" equalizes the voltage at a standard 10% less than the optimum, i.e., 110v here. If there's a line drop in voltage, the device is able to "reset" itself to deliver the lowest voltage required.
As to caveats... they have to be purchased for the specific type of device to which it is attached. In other words, you can't buy one for portable electric heater, for example and expect it to work on your fridge. To do so, even though the "plug" is cheaper than the one for the fridge, would harm the fridge. Secondly, they are fairly expensive. One for a fridge here is about $250 U.S. It would take about 2 years to recoup the cost through the electrical savings.
Newer, motor driven appliances, such as fridges, have circuitry designed into them to internally equalize the voltage automatically. You've probably reached the limit on your fridge and the newer ones are much more efficient. (Keep in mind that side-by-sides cost nearly 25% more to operate than top or bottom freezers). At any rate, best of luck!