US to UK Power Adapter (Wires Crossed)

Hi. I'm taking my US laptop to the UK where the power is 220V at 60Hz. The voltage isn't a problem because the laptop's power adapter will work from 100-240v. I was wondering if it makes a difference if the Live and Neural wires on the plug are reversed? Both countries use Ground (Earth), Live, and Neutral.

The Radio Shack adapters are "straight through", so the US Live wire will align with the UK Neutral, and the US Neutral with the UK Live. This appears to switch the polarity of the wires.

I don't have a background in electrical engineering, so I need to know if it matters that the Live and Neutral wires will be reversed.

Thanks!
~Dom

It's AC, no real problem since most laptop wires are just live and common no ground. Should be able to use practically anything there without problem. And you probably have a laptop with an unpolarized plug anyway (if it is made to work in japan, it's unpolarized), so you probably don't know which is which anyway.