I learnt this in about 1959, probably through the Heritage Society in Oxford, but sadly I don't remember from whom. Anyway it's clearly a fair bit older than has been suggested. I'm somewhat rusty these days, but so far as I can recall it went something like this. If I remember any more words I'll post again, or some of my contemporaries might if they read this (Mike Sutton?)

The borscht no longer bubbles in the gorschkies [?]
The samovar does not boil so loud and free
The schmielchiks [?] bow their leedle heads in sorrow
For love has gone from Olga…
   … and from me.

Olga was a true Siberian maiden
She was jealous, in a jealous Russian way
She used to take me punting on the Wolga
          [right, that settles it, it was Oxford]
Now Olga's in the Wolga for to stay.

My friends they used to say I was a sadist
I used to pluck the wings from leedle flies
But that was till I met my daaarling Olga
And saw the masochism in her eyes.

It was cruel being kind to leedle Olga
          [that line needs changing]
Into her eyes there came a Russian glow
But when she used to whisper "Sergei... wheep me!"
I smiled a Russian smile and answered No.

It was cruel being kind to leedle Olga
At times it made me sad, I must confess
So when one night she whispered "Sergei... DROWN me!"
I smiled a Russian smile and answered Yes.

…………….

[pianissimo:]
The borscht no longer bubbles in the gorschkies [?]
The samovar does not boil so loud and free
The schmielchiks [?] bow their leedle heads in sorrow
For love has gone from Olga…
   … and from me.