I'm a named driver on two other vehicles and I am covered 'comprehensively' ie for accidental damage, fire & theft an third party on those vehicles.
If I drive someone elses car under my own insurance policy ie. I am not named on the other persons policy, then I would only have TP cover only.
Your friend should ring his insurance company and ask for a quote to add a temporary additional driver for a specified period, stating that he wants comprehensive cover for you. This assumes that he has comp. cover already himself (?).