Converting appliances from 120v -> 240v
Here is how manufacturers make an appliance one voltage or another.  


electronic switch-mode power supply. These can input a huge range of voltage, for instance many fluorescent ballasts take 90-306V.  If you see that, don't be surprised, it really works. 
The machine runs on low-voltage AC or DC from a pluggable "wall wart" transformer, and they simply give you a different transformer for different voltages. 
Internally, the machine has matched sets of 2 things: heating elements, motor windings, etc.  For 120V, they connect the two things in parallel.  For 240V, they connect them in series.  Sometimes there's a switch on the outside, otherwise you might have to tear into it. 
The machine's key components are wound differently with different wire, e.g. 120 turns of 2mm2 wire for 120V, 240 turns of 1mm2 wire for 240V.  These, you cannot convert in any practical way, except to buy different parts or more likely, a whole machine.


Keep in mind: In the UK, many power tools are 110V.  Construction sites are set up with special 110-volt center-tap transformers (55 volts per leg). A hot-to-ground fault is far less dangerous than their normal 240V. 

I would bring over a good supply of 12 AWG extension cords so you can leave the autotransformers in one corner of your shop and bring the power to the tool.  

If you just wanted to wire your house with a 120V sub-panel and NEMA 5-15 outlets, used 240/480 input, 120-240V output, 5KVA transformers are often pretty cheap on Craigslist. That's not a consumer product but is for permanent installation and could power a small (40A 120V) sub-panel. 

Also for bigger tools, you may be better off using Euro tools. Their receptacles can deliver twice as much power as our little NEMA 5-15, which limits common American tools.