no REPUTABLE hire car company will hire you a car without a card. Some dodgy hire car companies who dont service, mot or repair their hire cars will hire them to anybody.
AVIS, National etc etc will ask for a card, end of.
Choose a firm for long term car hire, who focuses on your credit worthiness based on internal scoring system that only focuses on your present circumstances and your projected future as opposed to the standard credit scoring criteria that focuses on your history.