Hi Barry,
I have over the years cleared several drains and sewer pipes. No hassle. No dirty Hands and no mess.
Available off the shelves of Woolworths or Coles is the secret. Sodium Hydroxide, or caustic soda.
Pour the whole 500gms into the blocked drain. Wait a few hours or sometimes minutes and it suddenly flows free.
The worst I had was a sewer pipe. I used two lots to clear it and 3 hours wait. Better than getting dirty.
Just don't let the stuff touch you, its pretty mean. Incidently Drano is about 50% Na OH.
Cheers Marty