Surely if the policeman did more than one thing, it would be actions?No, "action" is fine, but so is "act".
"Act" implies that he did one thing that saved the lives. It may well be appropriate - if he threw himself on a gunman, then that would be a single act.
"Action" implies that he was running around doing things (see "take action" for the context of "action" in your sentence). He might have thrown himself on a gunman, wrestled him to the floor and yelled at the passers-by to get out of the way, then hand-cuffed the gunman and called for back-up. That's not just "act", that's "action".
Considering the two scenarios I have described, "action" would be ok in either cirumstance, "act" would only be appropriate in the first.