"Unable to see a GP"

The GP practice that we are registered with couldn't provide an appointment when I rang for my child. We then changed practices and he saw one of the doctors the next day after registering and had blood tests straight away, he was then sent to the hospital for further treatment. Had we not changed to a practice that provides urgent appointments he wouldn't have received the treatment he urgently needed. I can't understand how one practice can provide appointments and his previous practice can't, we were told nearly three weeks wait to see one of their doctors at Southlands Practice, this really is far too long yet at the new Practice we were seen immediately.