so are all of those horror stories about people blowing fuses and their hair-dryers just due to cheap transformer/converters, then?
On the whole, I'd say yes. Either that or trying to run with a transformer which is too small for the appliance (hair dryers take a fair amount of power).
The waveform you get from your wall outlet is a sinewave, so named because it follows the mathematical sine function. If you plot the voltage against time, it looks like this:
A similar plot of the power you obtain from some of the cheap & nasty converters looks more like this squarewave:
I won't go into the technical details as to why some appliances don't like running on that type of power, but you can see how the waveforms are quite different.
When you use a standard transformer, you get a sinewave just like the one from the wall outlet, just at a different voltage. The only difference between the 120V power from a transformer in the U.K. and the 120V power from a wall outlet in the States is that the frequency is different: 50Hz here vs. 60Hz (cycles per second) in the U.S.
While there are a few devices which won't run properly on the wrong frequency, it is much less likely to cause problems than the sine/square issue.
Will those links you posted be safe with computers, too?
Yes. All modern computers will run fine on either 50 or 60Hz power.
I'm not that familiar with Macs, so I can't comment on whether single/dual-voltage power supplies are common or not, but if you can't switch the computer to 240V directly, then using a suitable transformer from one of the above links to drop down to 120V will be fine.
