I hope you don't mind the correction for your question, but instead of "most quickly," you want to say quickest.  At least in this context...  Anyhow, to answer your question!  I'm a native of California, USA.  I now live in Texas.  I can't speak for any other English speaking country as I have never visited one.  What I can tell you is that we have many different ways of speaking English in the USA, and they also blend into one another.  Some people use different words that we occasionally have to define for one another, which can sometimes slow us down.  HOWEVER, some people here speak slow and, some speak VERY quickly.  Take for instance people who speak both English and Spanish fluently.  People get used to speaking very quickly in Spanish, and so do the same in English.  But this also applies to monolingual citizens.  Hip-hop culture plays a part for some people, because of fast rappers like Busta Rhymes.  I myself?  Sometimes I speak so fast all of my friends don't understand me.  Sometimes I've been language studying for so long that my head hurts and I hardly want to speak at all.  Now that I've written you an entire book, the answer is: how can you really tell?  Too many different people who are different from one another.

I've been all over the USA, Canada, Britain, Ireland and Australia. The accents are very distinct, however I have never noticed a culture speaking faster.