I don't know of any company that actually offers their own cover for both accidents and breakdowns. Post Office insurance, for example, will provide policies that cover both areas of insurance but that's only because they act as brokers for insurers such as CIS and for the RAC. (i.e. what appears to be a single policy is actually two separate policies with two different organisations that have no contact with each other).
Similarly, the AA's insurance arm simply acts as a broker for other insurers and has no connection with its roadside service.
Further, while both roadside insurance and accident insurance can offer no-claims discounts, they're completely separate. So, for example, the fact that a motorist has recently suffered a clutch failure, an alternator failure and a blown head gasket should have no bearing upon the validity of his claim in the event of an accident (or on his NCD for his accident cover).