Insurance usually comes not from the card issuing bank but from the entity through which the card is processed such as Visa or Mastercard. Visa/MC insurance is secondary insurance meaning that it supplements other insurance you may have. Personal auto insurance policies do not necessarily cover rentals and if they do, they rarely cover rentals outside of your own country. You should confirm what coverage you may or may not already have.
If you use Visa/MC insurance for rentals while traveling, it will be your responsibility to pay all damages, to deal with the rental company and any injured third party. Visa/MC insurance only reimburses you and the amount may or may not be your actual cost or loss.
Those in the UK can purchase rental insurance at very reasonable rates through companies such as
Insurance 4 Car Hire or
Car Hire Insurance. Those from the US who have American Express cards should look into
AmEx insurance for $25 which covers almost any eventuality.