There are several carriers that will insure you with a foreign license
. In California, you will need to provide both your foreign license and your US permit information. One of the rating factors in California is driving experience. Since you've had your UK license since 2012, you want this to be taken into consideration for your driving experience. Only having a permit in the US will impact your rates but again having your foreign license will help not to impact the rates as much as if you were just now driving.