I often see IPA representations of words (e.g in Wikipedia) that render the American accent of English (instead of British). Is there any agreement on which English accent IPA should render or does it depend on the authors native accent?
IPA can be used to render any dialect or accent you like. (Here's an example where IPA is used to show differences between two dialects of English.) It can be used in a narrow way, transcribing more precisely the sounds of a particular accent; or in a broad way, ignoring certain distinctions in favor of larger features.
English itself has no standard dialect, anyhow. Even the high-level split between American and British English is far from sufficient to describe how English is actually pronounced across the globe.
Now, there's the question of what exactly constitutes "British" English: is it RP, Estuary, something else? It's usually taken to be RP, so let's go with that.
The agreement is basically: do what standard you adhere to, better if you know both ways. Nothing forces you to use General American over RP or vice versa.