That's the difficulty - no, I don't have an acceptable form of alternative ID. They accept a passport or national ID card (which the UK does not issue).

Since I speak German with a non-standard English-speakers' accent, I have been asked several times to prove my citizenship.

A driver's licence is not acceptable, as it doesn't prove citizenship. My Australian passport does not show any right of abode in the EU. So I need to keep an EU passport (at present, UK) with me at all times.

Therefore I either have to wait to get my Irish passport (which I'm getting in the wake of the Brexit vote), or apply for the Russian visa as an Australian.