car rental insurance in the UK

The vehicle's owner has a lot more assets at risk than you do, so they have the liability covered cold. All you'll be insuring is the cost of repairs to the vehicle you're renting. It's not an issue for you to worry about.

what if the accident is my fault? In California the person who is at fault is responsible for damages tot he other vehicle/passengers.

What Ed said ... Liability covers the damage to someone else's property. The owner of the car (the rental company) provides the liability coverage. What is not covered is collision damage to the car that you are renting. That is the cost to repair the car that you are driving. That is the additional coverage that you need to protect yourself.

Actually, the driver has the most exposure. If you are a driver involved in an accident and are at-fault you need to make sure you have sufficient liability insurance for injury to other parties, including your own passengers as well as the other vehicle occupants, as well as property damage to others. I would suggest you verify, before you go, what the rental company's basic liability limits are. I am not familiar with UK rules, but generally rental car companies maintain the lowest coverage with which they can get away. They are not exposed for any excess, the at-fault driver is. I find most people are worried about the damage to the rental car, which is important, but it's the liability coverages that are even more important, as those are the claims that can ruin you. Ola, it seems you already knew this, but the other posters did not appear to understand. You can buy more than the basic rental car liability coverage. I suggest you contact the rental car company for their additional optional bodily injury coverage options and property damage to others coverage. Otherwise, I'd check with your insurance agent to see if there is a special temporary policy you could put into affect to cover automobile travel in the UK.