Can I insure a rental car through a insurance company?

Most rental companies include third party liability and some accident damage as standard and then try to sell you excess waiver insurance typically for about £25 a day. This insurance can be bought separately for about £4 a day online, which is what I always do. It also normally covers tyres and glass which the rental co rarely does. Down side is you have to pay for the damage and then reclaim it.

The default of taking the insurance offered by the rental company is better than not having insurance at all, even though it is expensive. Hunt around, using the suggestions in other answers and other things you think of yourself. Joining AAA and finding out what they can do for you immediately comes to mind.

Try State Farm.  They have a policy that covers unlimited rental cars with liability and comprehensive and collision coverage.   It is kind of new.  If the agent is not aware just ask them to check with their auto underwriter. 

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Most insurance companies exclude rentals. Take the insurance offered by the rental company.

You do have the option of obtaining "Non owners insurance". 

However, you would be better off, as far as both coverage and cost, to simply pick up your desired coverage directly from the rental agency. 

You may buy "Non owners insurance". It covers any vehicle that you do NOT own and that you drive with permission.......BUT.....It only covers for liability. Not all insurance companies offer Non owners insurance.

No, you can't.  Not with a standard auto policy.

The big thing with car insurance is the Liability coverage, not the vehicle itself.  The owner (not the driver) is legally responsible for any loss or damage their vehicle causes.  You're not the owner of a rented car, so companies like Geico or AAA or whoever won't issue a policy for you.  You have "no insurable interest" in the vehicle.

The insurance you're looking for would cover your responsibility for any loss or damage to the vehicle you rent, and that's expensive as hell.  If it were available through regular insurance companies, it would cost just as much as Hertz and Avis charge.

NOTE:  Have you looked into a long term lease?  Depending on how often you drive, it might be a cheaper option.  And leased cars are treated like owned cars (with a few technical exceptions) by regular insurance companies.

It's not worth the effort. Just get it from the rental company.

I doubt it, because you do not own the vehicle. You have to buy coverage from the rental company.

Perhaps you should CALL THEM and ask.