I had a curling iron that didn't make it 
Melted clear off the plastic handle.
It would. On a simple heating element doubling the voltage also results (more or less) in the current doubling as well. Since power varies with the square of the current, that curling iron was trying to give off
four times as much heat as it was designed for!
But to the technical points on washer/dryer electrical hookups.....
There is the usual American 120 vs. British 240 volts issue on washers. A step-down transformer could be used to get around that, but there is still the frequency difference, 50Hz in the U.K. vs. 60Hz in the U.S.A. Transformers alter voltage, but not frequency.
While this isn't generally a problem for the types of smaller motors found in mixers, blenders, etc., the difference becomes much more significant on the type and size of motors found in larger appliances like washers and dryers, so the motor would almost certainly be running less efficiently and would quite probably run hotter than usual, not to mention running slow. Some programmers also use a small synchronous motor to operate the timing cycles, and that would also run at 80% of normal speed, thus extending all the cycle times.
Dryers have all the same problems with the motor/timer over the frequency difference, plus some extra hookup difficulties. A lot of people don't realize that American homes have both 120
and 240 volts available, but the higher voltage is used only for heavier appliances such as heating, air-conditioning, electric ranges, etc.
Your American dryer plug might have either three or four prongs depending upon when and how it was installed, but both types provide 120 and 240V for the dryer. 240V is used for the high power to the actual heating elements while the 120V runs the lights, motor, timer, and so on. To run this on a British supply which is straight 240V you'd need to fit a transformer to derive the 120V for the controls. But you'd still have the frequency problem to contend with.
In short, unless you have a lot of time, money, and/or expertise to convert everything, forget it. There are "American style" washers and dryers available here which are designed for 240V 50Hz if you want the larger capacity and have the space.
Yeah, I know, Paul went off on a long technical ramble again to come to such a simple bottom line, but I like to be reasonably thorough with my explanations! 
