yes to both for me (my laptop and my iPod nano), and they'll be fine. The iPod works with a UK computer just like a US one. Most US mobile electronics are perfectly compatible with UK electrical systems (as in, they're dual-voltage)- check your adapters to make sure though (should say something like 110-240V, if it does you're good to go.)
You'll just need either a basic plug adapter to make the cords fit to UK plugs, or buy new UK adapters/cords from the shop.