Sycamore,
"I assume the `Fuel pressure`warning is taken from the supply tank to engine line," Correct - at the engine end
"and also assume that irrespective of other captions/cautions /indications,the `prime` switches are put on immediately.(as they were found to be ). Not exactly - If there is a fuel pressure caption in flight then, the first action after establishing that the engine is still running is to check the associated supply tank contents. If there is fuel available in the tank then it indicates that either the engine driven pump has failed or you have a leak. The purpose of putting the prime pump on is that if the Fuel Pressure caption goes out then it has proven that the engine driven pump has failed. If, however, the Fuel Pressure caption remains on then you have a fuel leak. If there is no fuel in the supply tank then there is no point in putting the prime pump on.
Are there any other actions to be taken as well...?
Commence drill for single engine shut down unless you are already finals to land.