Up until fairly recently, almost all insurance policies (irrespective of whether they were 'fully comprehensive' or just 'third party') allowed the policy holder to drive any other vehicle with the owner's permission. The cover provided was always 'third party only'.
However, the insurance market is now so competitive that insurers are trying to find more and more ways to keep their premiums below those of their rivals. For this reason, some insurers no longer include 'third party/any vehicle' cover with their policies. The only way to know whether a policy includes this cover is either to ask before taking out the policy or by reading the small print of an existing policy. (My 'third party, fire & theft' policy, through KwikFit, still includes 'any vehicle' cover so not all insurers have withdrawn this facility).
Chris