It's a little confusing for the layman since different people use the term "converter" in different ways.
The item in the Maplin link you posted is just a plug adapter or converter. It will allow an American plug to be connected to a British wall outlet, but it does not change the voltage. Simple plug adapters like this can be used if the U.S. device will accept the higher voltage, e.g. a desktop computer which has a 120/240V selector switch on the rear, or a typical modern laptop power supply which will accept either voltage without adjustment.
However, if the device you are connecting will run on 120V only (as shown on the tag/label), then you need a step-down transformer, such as the types shown on the Airlink and Newmarket links, which will convert the British 240V supply down to 120 volts. A lot of the "wall wart" power supplies (plastic box which plugs straight into the wall receptacle) supplied with computer peripherals, phone chargers, etc. are 120V only.