Keep in mind that there are two types of rental car insurance you can get through your credit card. Most cards include as a "benefit" free rental car coverage, and then some cards offer a premium coverage, which you must enroll in, and pay an additional cost for, when you rent a car. AMEX Premium Rental Insurance is an example of the latter, you pay a flat fee for the rental, others may charge by the day or week.
To me, it is get what you pay for, I do not rely on the free coverage, if you do, then understand what is covered, what insurance you must decline from the rental car company, and what the claims procedure is. To just assume you are "covered" will likely mean in the event of a claim you will not have something like a Police or Damage report, and you will be fighting with both the rental car company and your credit card.
I do use the AMEX premium on some rentals, including the UK. In other Countries like Italy, I take the rental companies insurance, full coverage.