"my council says it has a no kill policy and rehomes all healthy, non dangerous dogs."
And there you have the answer, Klad.
Aside from the fact that a no-kill policy is not one at all unless it is genuine and all-emcompassing except when the dog is suffering incurably a pound's definition of "dangerous" and "healthy" is at best variable and at worst pretty bloody appalling.
I know of pounds which will kill dogs which come in with or subsequently develop kennel cough. These go down on council records as "destroyed owing to ill health" if you care to make a FOI request but as you probably know it's stretching the truth to the point of taking the piss. Kennel cough, as you doubtless also know, is entirely curable with a simple course of ABs. Sometimes you don't even need that, depending on the severity of the case and the likelihood of cross-infection in multi dog households.
The problem with kennel cough is that it spreads like bloody wildfire. A dog with it could easily infect the others in the pound and then you're looking at a rapidly increased vet's bill. So what's cheaper? 20 courses of ABs or one single injection of barbiturate?
I know pounds which do this.
I also know pounds - one in particular - which routinely kills GSDs, Staffs, Rotts, Mastiffs etc at the end of their legally demanded 7 days in the pound as they won't spend the time trying to work with rescue to get them into safety.
And "dangerous" dogs?
Those who are considered dangerous in the legal sense won't be in your local pound - those awaiting court cases under the DDA will be in a secret location. YOUR pound's definition of "dangerous" is... what... ?
A dog which is so frightened of being in the pound, amongst the smell of fear and other dogs, far from his home humans he knows, that he growls when someone approaches him? So they say, "I can't get near that dog, can't risk it, haven't the time to sod around with him" and mark him down for death when the vet comes round next morning.
So many of these dogs are only deemed "dangerous" because it's a fuck site easier and cheaper to kill them than to work with rescue to place them in safety once their 7 days in the pound are up.
I've got one of those dogs right here. Couldn't get near him, no-one can, 3 years down the line the (lovely) rescue owner STILL can't! But he loves me to bits... because I'm a rescuer and he went to a genuine no kill rescue where i took the time to work with him, determined that I'd overcome his fear... and I did, he's been here a year now.
Believe me, I've fought to get what must be hundreds of dogs like him out of the pounds. Dogs which weren't "dangerous" but just pure bloody frightened. I've saved hundreds too. Every single one that I could get to the safety of no-kill rescue I did get to safety... and the faces of every dog that the bastard pound managers refused to release to rescue despite my pleas and instead ordered to be murdered will haunt me for ever.