The Dogs Trust never destroy a healthy dog because they don't take in every healthy dog.
The RSPCA will try their very best to find your dog a new home. They're not Nazis and plenty of people do go to the RSPCA for a rescue dog. But the RSPCA are a charity and can't take care of every unwanted...
Just want to add to this thread that if you're ever thinking "ooh getting a dog would be nice", please think it through very very carefully. They are for life and there is no easy way of rehoming a dog.