I think there should be an easy to remember non-emergency number. Although, that would require a certain judgement about whether the situation was an emergency or not.
Case in point:
I was driving along the A38 from Cornwall. I was behind a car for sometime, and after a while, it became apparent that the car was travelling forwards, but was actually pointing towards the right hand side of the road. It took a while to be sure I wasn't imagining this, but it was obvious the driver kept having to correct the trajectory to keep the car going forwards.
Now this wasn't an emergency as such, no-one was dying no-one was trapped or on fire - but, how long before the situation changed into something serious ? *
So, after a deep breath, I called 999 on the cab phone and asked for the police. I explained the situation and after giving as much detail as possible, they kept me on the line while I followed this car for about 10 or 15 miles, me giving them updates on where I was. Eventually, I lost sight of the car, as it speeded up to over 60mph on a dual carriageway, even though it was obviously defective. But the operator said it was ok as there was a car behind it now. Sure enough, I came over a hill and found the car had been pulled over and an irate looking driver was standing at the side of the road waving his hands about. Job done. I comforted myself with the thought that the police had probably waited until they were sure that the car was displaying the symptoms I had described before pulling it in.
Anyway, about 20 minutes later, the phone rang, and it was the police operator. Oh shit, I thought, I'm going to get done for wasting police time or something. But no, he was just letting me know the outcome ! Apparently, the car was damaged in some way, and the driver was a "trader" ** who was trying to get the vehicle back to somewhere he could get it fixed. I was thanked for my call, and went about my business.
Overall, I would classify the whole experience as bizarre.
So the police do take action if they can, and are even quite polite about it.
* I have been driving a car that showed no bad symptoms, which, when I went around a left hand bend, suddenly lost steering because the right hand steering joint broke. I immediately hit the brakes, but because the RH front wheel was no longer attached to the steering, it flew back against the wheel arch and locked, causing the car to spin in a clockwise direction, right across the path of oncoming traffic. So bearing this in mind, I felt that the situation could easily become an emergency, and why wait until someone was dead or injured just to prove my point.
** Surely a trader would have more sense than to drive a car that could let go at any moment, at speeds of over 60mph on public roads. That's why they have recovery trucks.