It took us 21 months (from referral) to get a diagnosis for DS that was 12 years ago, now it's less than a year, there was also a13 month waiting list for OT and PT, now the waiting list is under 12weeks.
last year our eldest got a diagnosis of autism after a 12month wait.
When I was a child the children who were diagnosed with Autism were sent to special schools as were the children with Down Syndrome, Cerebral Palsey etc as well as those with other physical disabilities, the children with severe learning disabilities were classed as uneducable and didn't go to school they went to day centres a couple of days a week.
Asperger's Syndrome wasn't used as a diagnosis before the mid eighties and only became a more widespread diagnosis in the nineties, it is now falling out of use because the DSM V no longer lists it as a separate diagnosis, it is now diagnosed as Autism.
Someone upthread (sorry for not naming the pp) wrote a label is something that you put on a suitcase, I totally agree and have used that same sentence (under different names) since I joined Mumsnet about 6 years ago. I'm sure that I have also stated that you find labels on jam jars, tin cans and bottles, I've definitely stated that no other medical condition is referred to as a label, a person with Autism has a diagnosis not a label.
As for institutions there were many different types, most people didn't need to know about them, where they were, what they were for etc so would have had no idea what was available with the exception of the local 'mental hospital'
The earliest medical reference to Autistic Behaviour I have seen was dated 1913 However Autism has undoubtedly been around long before then.