I have ordered the new USB board for BV6000 on Aliexpress and replaced it.
But it did not help at all.
Finally I have found the solution on Russian 4PDA site.
The capacitor is missing on the power line of original BV6000 USB board.

It is necessary to install at least 1uF capacitor (16V).
Now OTG works just fine. I have tested few USB flashes and the wireless mouse which did not work before.
Some people on 4pda site suggested to install 1 or 2 diodes in parallel with capacitor (note the correct polarity).
They got an external HDD works after this mod.