Around here the police have just announced a new initiative. Get burgled, robbed, mugged etc. and the police simply don't care enough to send officers around, you have to phone up a 'resolution centre' instead.
http://www.stokesentinel.co.uk/news/stoke-on-trent-news/ello-ello-ello-police-now-1153930
The media are quick to spin this in exactly the way you've interpreted it (where the police are portrayed as not caring enough to send officers or do their job properly etc), but the reality is somewhat different.
Rather than having a 101 or 999 call centre that can only handle enquiries and create incident logs to dispatch officers too (which was all they used to do), most forces are now starting to train their call centre staff so that they can now complete and record crime reports over the telephone.
Back in the day, only a police officer could generate a crime report, the call handlers were not trained or allowed to do it (both for reasons of knowledge and understanding, and home office accounting rules which forces were routinely slated for if they did not follow, whether through administration errors or deliberate efforts to massage official crime figures to make themselves look good). When officers were plentiful, this was less of a problem. In times of austerity when police numbers have fallen, whilst demand for service has increased (significantly so, partially due to the growth in mobile phone use over many years), it is simply a numbers game where the forces do not have enough officers to send to every call for service.
What the 'Resolution Centre' is meant to do is properly triage the calls as they came in, and generate crime reports/crime numbers over the phone where appropriate. Call handlers are trained to ask more questions and take basic details about an alleged offence, and can either record the offence over the phone or can forward the job to the dispatchers who can direct police officers to attend directly, depending upon the nature of the crime and the opportunities to gather evidence. The questions will help decided whether there is actually any points in officers attending.
What this means is, your hypothetical high value car key burglary with CCTV, forensics, witnesses and evidence left at the scene will *still* get officers dispatched to attend and deal with it and investigate it properly and thoroughly in the way that people expect.
What it also means is that your lower level burglary or theft, say a garden shed that's been broken into, where there are no forensic opportunities, no witnesses, no CCTV and essentially nothing of investigative value, can be dealt with entirely by the phone. The victim gets a crime number and the case gets closed at source, when there no lines of enquiry to follow (The call handlers will ask basic questions - IS there CCTV? Are there witnesses? Did your neighbours see/hear anything? Is the property that has been stolen traceable in any way? Are there any obvious forensic opportunities or items left behind by offenders? If the answer to such questions is 'No' in each case, then the crime is unlikely to ever be solved and there is little that will be achieved by sending a police officer directly other than providing a basic level of reassurance).
When there's not enough officers to send, the rational option is to deal with some crimes over the phone where the actual presence or attendance of a police officer will achieve little of practical value (given that in many cases, there are simply no proportionate lines of enquiry to follow and thus no evidence for a police officer to gather). The idea is that it frees up officers time to go and deal with incidents where there is a real chance of gathering evidence and/or arresting offenders, rather than spending time going to deal with offences where there is no evidence and the only outcome is an officer applying some verbal 'There, There' cream, reassurance, and giving the victim a crime number.
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