Molly you are not late. Anything up to 40+14 - so 42 weeks - is entirely normal. The whole thing about "late" 1 day after EDD is nonsense, they should not call it an EDD, it's just an average guess date plus/minus 2 weeks either side is perfect.
In fact first babies more often come around week 41 plus/minus!! In France they estimate their equivalent EDD date at 41 weeks.
You don't have to do an induction if you don't want it. It's entirely your choice. As long as there is no medical necessity induction when the body is not yet ready can lead to a cascade of other interventions and lead further away from natural labour and be harder on both mum and baby. You can ask for extra monitoring if they are concerned about the state of the placenta, for instance, but at 40+10, knowing what I went through at 40+11 with my induction, I would now have asked why they were steering me that way. Docs are risk averse and want babies out ASAP not paying heed to nature much these days. Our bodies are designed for birthing - docs tinker with us too much at OUR peril. Hugs