Jonty - every one of us has sinned and has fallen. The only thing that saves us is the blood of the lamb.
I just recently made the choice to discern between “sin” and “dead works”, dead works being a subset of sin:
Sin: Disobeying God’s law.
Dead works: Doing good things to improve your chances of salvation.
In fact, Hebrews 12:1 nails it: “Therefore, since we are surrounded by such a great cloud of witnesses, let us throw off every encumbrance and the sin that so easily entangles...”
IMO, the “sin that so easily entangles” is the belief that we must “be good” to receive salvation, coupled with working towards salvation, rather than simply accepting it and then going forward knowing we are His heir.