The fundamental curiosity underlying this question was piqued by this provision:
And a wondering as to how often it is invoked, which raises two questions:
how and how often would the CPS learn of independent prosecutions?
And, what incentive do they have, once they do learn of them, to bother with taking them over?
These two questions would both surely be underpinned by legal provisions governing the surrounding processes, so these are what this question is directed at.