Hi Kate,
Our car insurance is through Zurich (UK company.) We got my car having been in the UK for one month. My DH can't remember exactly why he chose them, but they had no problems with insuring us, both US citizens, newly arrived to the UK. We pay about 79 pounds a month for both of us -- it's a bit higher than might be otherwise, but that's because my car is in a higher insurance rate category -- bigger engine, etc. They didn't seem to have a problem with us having US licenses.
Hope this helps,
Stephanie