OP just incase no one else has said it in the thread, you don't have to be induced. I read on one of your comments something about "they made the decision" it's your decision.
If you want more information regarding induction and your choices, I can recommend the NICE guidelines, AIMS guidelines, Dr Sara Wickham also has a website which is really helpful and a book called Inducing Labour which I read when I was considering induction it talks you through everything to do with induction so you are fully informed and can make an informed decision, if you do decide to go ahead with induction this book is amazing because it tells you exactly what happens during the induction so your not in the dark about the NHS processes and procedures. I think if you did decide to go ahead with induction it arms you with knowledge which makes it less scary because you know what to expect and what options you have throughout.
Also I would look into the accuracy of the scans, I was told when I had one (by the lady that did the scan) that they weren't particularly accurate but they are the most accurate way they have to estimate babies size... but this far along it's so inaccurate!
It really seems like you don't want to have an induction and I think for that reason it's important to make sure you know everything you can about it so that you can feel confident having one is the right decision or not having one of the right decision.
I went to 40+12 and I chose not to have an induction personally, this was the right decision for me but it was a hard decision because I do feel a lot of pressure was put on me to have one, even though I made sure that I did a lot of research to demonstrate an informed decision, they were still pressuring me aggressively for no other reason that she didn't come on the date that they estimated. This really upset me and didn't change my mind because I knew in my heart that for me it was the right thing to do. But they basically ruined the end of my pregnancy because I was so stressed.
Really thinking of you OP because I remember what this was like, please remember you always have a choice. Also, if you make the decision to wait, I found the Facebook page Ten Month Mamas gave me so much emotional support, so just to recommend that too if you go in that direction.