LineRunner, Battersea is a pound, where the councils take their strays. A rescue is a completely different establishment.
Battersea do rehome and are pretty good in their procedure from the POV of an adopter but they kill healthy dogs because the law says that councils need only keep strays for 7 days. After that councils may rehome, send to rescue or kill those strays. The law says that a dog handed in by his owner may be killed immediately.
So of course councils only pay their operators, the pounds, for 7 days care of the dog. Many pounds are profit making organisations and not run by the council - boarding kennels often have their council's pound contract.
Hence pounds kill healthy dogs after 7 days because they can not or will not keep them at their own expense. Some pounds will cooperate with rescue more than others, some are bastards.
Anyone know Fleet Boarding Kennels in Yorkshire? They automatically kill Staffs, Rotties, GSDs, Greyhounds and any other large breed or type they consider hard to home, on day 7 without even trying to find rescue places for them.
Any pound which says that they don't PTS is lying.
They do... they don't rehome those which they deem aggressive (even if only through fear of being in a kennel), they don't keep alive the vets bills on legs for more than 7 days as they would have to pay for a lot more than food and water if they did.... they make an economic, not moral decision.
They leave the morals to us in no-kill rescue.
(Polite word of warning - be careful not to confuse a pound and a rescue. Sod that the title is Battersea or Manchester "Dogs Home" (bitter irony there), that's just a title. Ask them outright if they have the contract for the councils strays. If they do they can cry rescue all they bloody well like, but they're a pound).