Just in case this is of use to anyone else -
Having not had any response from Arisa or AXA, I got a bit worried towards the end of my time in Russia. I had got a German friend to check with the ADAC, who said they could provide Green Card cover within the EU to a UK-registered car (but it would be expensive). I then spoke to a Latvian insurance company, who said that only Latvian or 3rd countries (non-EU) citizens could buy insurance on the Russian/Latvian border. They said they used to sell insurance to cover ALL EU nationals as well as non-EU, but had to stop as of November last year as they were advised it was 'against the law' - whether that was Latvian law or EU law I don't know, but my understanding is that EU law means members of every EU member state should able to buy EU car insurance anywhere in the EU, so if that insurance company is following Latvian law in precedence over EU law on this then it may be wrong to do so. Nevertheless, the British Embassy in Riga also confirmed what the Lativian insurance company had said.
I also tried AIG's office in Moscow – they provide Green Card cover from Russia for EU countries only for Russian-registered cars (although readers may like to note that Russia will be joining the Green Card scheme on 01.01.09, so buying Green Card cover from Russia will be just the same as it should be from anywhere else in the EU).
I really couldn't understand what the problem was with me not being able to get Green Card cover at the Latvian border, so I took the number of the ADAC with me to the border, ready to call them to activate cover if I got refused by the Latvians. But would you believe it - I went to the booth, showed them my UK registration certificate and passport and they sold me a 1 month Green Card policy!