I don't know about the RSPCA but I done some of my training time at the Scottish SPCA and they had a 10 day thing. Healthy animals were never put to sleep but after 10 days they could be rehomed.
Many animals had been there for a long time.
A very upsetting part of life
I believe legally they only have to keep them for 7 days although this is not the case if its a cruelty case where a court has to decide whether the owner can keep them, but if they are strays it is 7 days.
The RSPCA is not responsible for strays-that is the local councils responsibility through the dog warden. Dogs come in to the RSPCA mainly through the Inspectors as welfare cases or from a waiting list of people who have arranged to sign them over for a variety of reasons eg people going into sheltered accomodation or residential homes where they cant take pets. They are put up for rehoming as soon as the vet has passed them as medically fit and they have been assessed for any behavoural problems so the time varies from dog to dog. Some spend time in foster homes if they are not coping with kennels or need to recuperate after an operation. Some poor dogs spend months even years in kennels waiting to be adopted.
My own dog was in RSPCA kennels for six months before we found each other. Like some of these posts say, many, many dogs spend a lot of time waiting for a home. Too many poor unwanted dogs and not enough homes and yet breeders are allowed to bring even more into the world, Doesn't make sense to me. If you want a dog, rescue one - simple.