I need U.S. car insurance for my British Land Rover. It is a 1988 model with British plates. I need short term insurance 6 months or so and am 75 years old and will be traveling in the California area.
Disclaimer: I am not a lawyer, nor am I a California resident.
However, I would not expect you to be able to insure your overseas-registered car with a California insurer. In every state that I have lived in, insurance companies require you to register the car in that state (and there's a circular dependency, in that states require proof of insurance before they will register the vehicle).
That said, the California Department of Motor Vehicles website describes the financial responsibility requirements for operating a vehicle in California, and it appears that you would be OK if you (1) provide the DMV with a $35,000 cash deposit, or (2) use a registered bonding agency to post a $35,000 surety bond.
Note that that is simply to cover liability, in case you cause an accident or damage property with your vehicle. It does not cover any damage to your own vehicle. Nor, to be honest, is it enough: I would recommend buying an umbrella liability policy from your local insurer. And you should also check with your local insurer regarding damage coverage (if that's important to you).
As for the legality of driving in the US with British plates, you should contact a US Consular office. I would expect it to be legal (provided you have liability insurance), given that there are lots of other countries within driving distance of the US.
Edit: although it doesn't say anything about foreign vehicles, AAA has a summary of traffic laws (with pull-downs for each state).
Also, the US AAA motor club has reciprocal agreements with the British AA club; it's possible they could provide additional information.