My time line was similar to yours. VFS doesn't give any information at all about how long biometrics take. I did dig up something from a guy in New York who said he got his passport back just a few days after biometrics. I also spoke to a girl from Iran at VFS who said it took about a month.
My timeline:
Applied May 18
Complained that there was no biometrics letter on June 23
Got biometrics receipt for payment later on June 23
Got messed around with payment June 23 - June 29
Was scheduled for biometrics July 1
No idea how long it will take now. Please respond if you get an update!
Note: this is for a visitor visa and it won't be my first, but it's the first one that requires biometrics.