let me help clarify this.
all nintendo ds systems, regardless of what region they are sold in, are the same (same battery). the only thing that differs is the ac adapter provided with them which regulate the amount of power provided by the wall sockets into the system based on the country they are sold in.
ac adapters
jp - 100-110 volt input (can be used in the jpn or the us interchangably)
us - 100-100 volt input (can be used in the jpn or the us interchangably)
uk - 220 volt input
so, as long as you use the ac adapter native to the country that your in (ie. uk ac adapter in the uk, regardless of where the ds itself was manufactured), you're ok.
if you want to use an ac adapter from another country (ie. you're taking a trip from one country to another (like the us to the uk) and are bringing along your ds, you'll need the appropriate step up or step down convertor to use your original ac adapter that came with your system. however, step up / step down convertors can be costly, so you might be better off purchasing an official ac adapter or better yet, if you have access to a computer in the country you're traveling to, pick up a usb power cable and use it instead. they're cheap ($5 or less) and they're your safest bet, since usb *always* outputs 5v no matter which country the computer is in.