I'm fascinated by this. In my native Russian, there's a children's counting rhyme "ene bene raba kvinter finter zhaba" (and the more popular "eniki beniki were eating vareniki").

You can see some resemblence of "ene bene" to "eeny meeny...", and "kvinter finter" to "tethera, methera".

I'm mostly puzzled how it was spread. How did children in Russia learn about this? It's not like it was very common in Russia to see someone from Britain, especially in the countryside.