There is no universal answer.
At one time the majority of insurance policies (both third party and comprehensive) permitted the insured person to drive other vehicles (with only third party cover) with the permission of the vehicle's owner. Even then, there could be additional stipulations within some individual policies (such as the vehicle not being owned by another person living at the same address or by anyone directly related to the insured person).
More recently, many insurers (in a bid to offer the cheapest policies possible) have removed 'any vehicle' third party cover from their policies. So some comprehensive policies offer such cover, while others don't. (Exactly the same is true of third party policies).
The only way to be sure whether you're covered is to READ THE POLICY DOCUMENT.
Chris