Yes, the voice is directly determined by your language/region setting for Siri. It's somewhere under Settings -> General. For English, you can choose between US, UK, and Australian dialects.
Each one comes with its own distinct voice, but changing that setting also completely changes the voice recognition, and the dialectic aspects of what Siri says and understands. So if your goal is to get Siri to talk with a British male voice, the accuracy will be less unless you also talk to Siri in (a passable approximation of some type of) a British accent, and perhaps also use British instead of American expressions, where relevant.
