This adds to what others have said.
This may not apply to UK driver / USA rental but is well worth looking at.
Taking out rental cover in your own country on a vehicle being rented in a foreign country BEFORE commencing the actual rental may result in far more favourable terms very substantially lower potential liabilities and/or lower charges.
This may or may not apply to your UK/USA situation but in the case of a New Zealand driver hiring a rental car in Australia, vastly superior terms and lower costs may be achieved by insuring prior to the rental commencing through either NZ insurance companies in NZ or through NZ branches of Australian insurance companies.
I'm "older" (or, my body is). I live in NZ and wished to insure a rental car in Australia in addition to the basic "cover' offered by the rental companies, as it left me with potentially very large liabilities. I am a scrupulous reader of insurance fine print, due to the major costs that may be hidden in policies. I found that rental vehicle insurance from Australian companies, whether taken out through the vehicle hire company, or Australian 3rd party vendors or directly from Australian insurance companies ALL contained extremely onerous terms and exclusions. Even in the 'best' polices there were worst case situations that could leave the hirer liable for most or even all of the rental vehicles value, even in situations where the cause of the loss was outside their direct control. [One extreme case - road collapse causing vehicle submersion or submersion at a "ford". Full vehicle value may be payable. Less extreme: Drive under truck-tray or overhanging ledge, or barrier arm.]
I then looked at the terms offered by NZ insurance companies for insuring the vehicle while I was in Australia. To my surprise, not only did NZ insurance companies not include the hidden super-onerous terms, neither did the NZ branches of the Australian companies. This applied only if I took out the insurance prior to the rental having commenced. Once the rental period commenced the NZ branches of the Australian companies would no longer offer the superior conditions. I assume this relates to anti-poaching arrangements between branches of the same company in different countries or even maybe within the industry,It MAY also relate to what degree the legislation in each country allows the companies to gouge their customers.
As a bonus, the NZ paid & arranged insurance for the policies with superior terms cost less in all cases than using Australian channels.
Crucial: Be super certain about what your potential liabilities are. Even if terms like "full cover" and "peace of mind total cover" are used in the 'large print' the fine print may contain (and in Australia does contain) far more onerous conditions.