Policy is something set by an individual force as opposed to law which is laid down for us. Policy can also be broken, if justified (and one must be prepared to justify, if necessary to a misconduct panel that break). Law can't be. In other words, in your story, decide if it's a policy of that force, then decide if the cops are going to follow it.
In my view, once again, pragmatism would be balanced by compassion and the victims wishes.
Assuming the victim wants her parents to know.
What if the parents live an hour into the countryside? Would it be fair to delay the parents receiving the news for an hour just to stay in-line with a policy document? Would YOU expect that when you could have found out immediately by phone? Do we have a spare unit free for the two hour journey, there and back? But receiving that news would be awful for any parent, let alone on the end of a phone. But what if they live five minutes around the corner from a unit that is free? But what about if the control room have two disorders, a suicide, a missing child, a burglary-in-progress and Mr and Mrs Smith are complaining again their driveway being blocked by a neighbour again (Take a wild guess at what glamorous complaint about lack of service I've been dealing with tonight!) on their screens waiting to be resourced?
But what about the rape itself? We may have a crime scene that needs to be guarded. We have the investigation to do, CCTV to view, forensics to consider, witness statements to take, telecoms enquirers to conduct, searches, house-to-house etc etc. All needs to be resourced as well.
And so on and so forth.
The short answer to your question, in real life is... depends! To quote the comedy show, Fresh Meat, your cops will have to either sh*t or get off the toilet in other words, make a decision.
Because, lest we forget, there's a victim there of one of the most horrendous crimes imaginable and she probably just wants her mum and dad and there's a bad guy out there who needs to be found and arrested as quickly as possible while ensuring we get the best evidence so he gets a conviction at court.
I would also say as a writer though you can remember that fiction policing and real policing differ in many many ways. Even on those cops on cameras programs, I've thought 'Eh? What are they doing?' (not that I watch them as I can't think of much worse than coming home from a hard day on the coal face to then watch a show about mining!). Unless you're marketing this book as a true police procedural... just try and get it in the right ball park.
In summary, as a Police officer would your described scenario 'throw me out the book?'
Nope.