Learn English – In which accent does Lieutenant Aldo Raine (Brad Pitt) speak

FrustratedWithFormsD's suggested indiscernible implies you're not aware of any accent at all. Which is increasingly common today. Just as genetically we're all becoming coffee-coloured people in this modern world of global communications and travel, so differences in regional accents tend to be "ironed out".

But OP wants a word to describe speech which is clearly recognisable as having some kind of accent - just not a "placeable" one. Perhaps because someone's speech combines two or more relatively strong accents in a way that makes it difficult for others to identify the components.

I'd call that a nondescript accent, as apparently would many others in that link.

According to the Pacific Rim wiki, Stacker Pentecost was born in Tottenham, London, and holds British citizenship.

I don’t know the movie at all, but the wiki also says he is the head of the Hong Kong Shatterdome, so perhaps his native British English has simply been influenced somewhat by Hong Kong’s colonial English accents.