English is taught in Israeli schools from primary school, and as you mentioned, foreign media is subtitled and not dubbed (except for media targeted toward children). Most people have at least basic or better knowledge of English and will be able to help a tourist. Also most public signs have an English translation, and many restaurants will have an English menu.
I can't say what is the English level among the Palestinians.
You might also have luck with other languages, 15% of the (total) Israeli population are immigrants from the former USSR, so you will probably be able to find a Russian speaking person almost anywhere. And in some cities, where the concentration of immigrants from France and South America is high, you might be able to find French and Spanish speakers. This addresses only the Jewish population of Israel, and doesn't hold true for the Israeli Arabs, or the West Bank.