I'm in a similar/same position when it came to insuring my Tesla last year and renewing it this year. It's a company car and on the V5 certificate it states the limited company name as the registered keeper. I had trouble last year doing it as not many insurance companies insured cars that had a limited company as a registered keeper, and it wasn't even an option when using price comparison sites. This meant you only found out they didn't cover it when you went through the process of purchasing it and confirming the details, which happened with Direct Line and LV. Nevertheless, despite getting some crazy quotes of £2k-£4k (Aviva being at the highest end) I managed to get it insured with Admiral for £845 (7 NCB, Bath and on street parking).
This year I used price comparison sites (Compare the Market in particular) and noticed you could select a company as a registered keeper rather than the usual options for an individual (e.g. you, parent, spouse, etc.). Funnily enough I received a wide number of quotes that included, Churchill at £860, Flow (underwritten by LV) at £950 and LV for £1.3k, there were no quotes from Admiral. At this point I decided to call Admiral about renewal who asked if my circumstances had changed and I said no, they initially provided me a quote of £1050 (with 8 NCB). I said this was disappointing as it was over a 20% increase from my current premium. They then asked if the two named drivers drove the car at all, and I admittedly said they didn't (added them originally to bring down the price), and then asked what the current market value of the car, I said around £43k (providing a number given by price comparison sites). They then came back with £825 (£250 voluntary excess), of which I gracefully accepted!
