By all means check with your UK company, but I am 101% sure they will NOT cover you. That's a purely North American feature and is why cars booked direct in the US are so cheap - just about all Americans are covered by their own policies and give misleading advice on travel boards because they assume it's world wide.
Check out booking through a broker here - Holiday Europe, Holiday Autos, Car hire 3000. They will have an inclusive rate including the insurance you will pay extra for in the US and often work out cheaper.
Or check this lot out:
http://www.carhireinsurance4u.com/
Slight problem is that I understand that if you have an accident you have to pay upfront and then claim off them. (Haven't checked all the fine print though so ICBW)