Hello, again!
Forgot to reply here about what happened.
So I was already in London one day before my supposed flight to Sydney still not knowing, whether I will be flying the next day. Decided to check my email at midnight just before going to bed, without any hopes about my visa. What a surprise revealed to my sleepy eyes. New email with a subject containing words "Grant Notification"! Yes, I received my visa about 12 hours before the flight Had a good vacation in Australia. Spent there 3 weeks, drove 8000 km.
I think that calling support in London did help, but they made the special mark only when 2 days were left. So thank you for the tips.