Virtually any third-party AC adapter is also going to have the same Input 100-240V & 50/60Hz as the Dell one, which means universal compatibility with the power lines everywhere on Earth. (Japanese 100V, Caribbean 110V, US 120V, Mexican 127V, Russian 220V, standard European 230V, old British 240V . . . most laptop/netbook AC adapters are designed to handle then all).
So, if you're buying an adapter that explicitly mentions that it works with the Dell Mini 9 in its description, and it covers the 100-240V range, then your only concerns will be the workmanship on the adapter itself, and the wall plug. The wall plug isn't a major problem; simple US or UK plug-to-Europlug adapters are trivially cheap.
For example, it looks like amazon.co.uk carries the UK version of the genuine Dell Mini 9 AC adapter (with the UK wall plug) for ₤10.99, and you can buy a UK-to-Europlug adapter for ₤0.99 at the same time.