Generally you're supposed to apply at the US consulate at your place of residence. So if you're a resident of a country you're not a citizen of (legally that is, and can prove your legal status) - you can apply at that country, regardless of your citizenship.
Otherwise they'll send you back "home" (the UK in your case), however in some places US consulates have been known to approve visas for non-residents (although from what I know it is not B2 visas, I know people who stamped their L1/H1 visas in Canada, not being Canadian citizens or residents).
To make sure - call the closest US consulate and ask them directly.
As a citizen of the UK (with the right of abode, IIRC that's how its called), you can use the WVP program and then you don't need visa at all, that provided you have a valid ESTA approval, and biometric passport, and plan on staying no longer than 90 days (without any ability to extend, under WVP its very strict).