It intends to provide these motorists with low-cost insurance over the telephone.
Direct Line insures 1.8 million motorists. But it has been 'cherry picking' - keeping down premiums by refusing bad risks. It estimates that about two-thirds of motorists are in the low-risk category.
They have to pay higher motor insurance premiums because they are considered higher risk, perhaps because of their profession, age or type of car.
Privilege hopes to be as successful with these motorists as Direct Line is with the better risks. But it will not insure everyone - a 17-year-old with a Ferrari would not be covered.
The new company will operate in the same way as Direct Line, with an interview carried out over the telephone.
Anyone who is refused insurance by Direct Line will be passed on to Privilege for a quote. It will also eventually offer household insurance to those who do not qualify for the standard rate.
The launch of the new insurance company is expected to increase the downward pressure on car insurance premium rates.
Privilege will be able to cut costs because it will not pay brokers' commission.