No, the information from your black box won’t be shared with a third party, except for the police.
And the police would only get access to your telematics data if they asked for it as part of a formal criminal investigation and legal permission was in place to allow them to access it.
However, it’s worth noting that if you’re the named driver on a telematics insurance policy, then the policyholder will be able to see your data and driving score. Something to bear in mind if you’re on a parent’s policy.