Keep in mind that the single item you mentioned is a transformer which, according to what you noted, will handle voltages from 110 V to 240 V and output 12 V. (What it doesn’t say is that it handles AC—alternating current—and converts it to DC—direct current). That is, it transforms from “high power” to “lower power”, and from AC to DC.
I don’t know what household current is in the UK, but in the US “house wiring” is normally 110 V (except for heavy duty appliances such as electric stoves, clothes driers and some air conditioners and other high-powered devices). In much of Europe and Asia “house wiring” is 220 V, so items that aren’t “rated” as you note, may not work at all, even with an adapter plug.
This is more of a problem when traveling with things like hair dryers, electric shavers, etc., from the US to Europe and Asia, where “lower current rated” items simply burn out when first turned on at 220 V.
It’s smart to look at what your appliance is rated for… and to know the current you’re attempting to use.
All your roommate needs here is a plug adapter, which is easily available at most hardware stores and computer supply stores, Radio Shack, and nearly anywhere else that sells electronic equipment.