A few observations to contribute to the debate;
They closed our village Police station, but instead opened up a little office adjacent to the school (not because the school has problems necessarily, but because it was convenient). Although being sceptical I have to admit that you do see Police presence around, and contact is possible. They also seem quite well engaged with the Neighbourhood Watch. We all have the 101 number in the country now as well. Our county was one of the trial areas and it seemed reasonably effective.
Two weeks ago I had a Member's assessment with the IAM, part of my self imposed regime of refresher training every few years
. You'll be pleased to know that the examiner (recently retired from Police) was keen for me to be doing shoulder checks in traffic to watch out for cyclists and motor cyclists.
On a more serious note, I know someone who had a domestic violence case to deal with recently, and she could not sing the praises of the Police high enough in the way the whole thing was handled (and followed up). And she is someone who has always been very sceptical of the boys in blue and had only involved them initially from a 999 necessity.
Like 661-Pete, my sample of experience is pretty small. No doubt some people have loads of experience.
(Admission of interest; I have had Police within my family. I can tell you the Police are human beings, and not always perfect...