Severe anxiety IS a medical condition. It also slows down birth, and leads to a greater likelihood of interventions such as EMCS. On top of your baby's size, your size, etc it seems like a very reasonable request.
The consultant is being a bloody pig-headed fool. It's likely she is thinking of the hospital's stats, rather than you. Don't allow her to sacrifice you to make the hospital look good. Push back HARD on this, OP.
Ring tomorrow and say you are unhappy with the decision, and want to see someone else ASAP as the refusal is causing you severe anxiety. Threaten to go straight to PALS if you are not made an urgent appointment to see somebody else in short order.
Read up on the evidence for and against CS, so that you can evidence you are informed and accept the risks. From memory, the risks are different to VB, but roughly comparable, though CS is overwll slightly less risky for the baby, but slightly more risky for you. It does raise risks for subsequent pregnancy, though, but they are still small. Only really an issue if you want more than 3.
You do NOT have to consent to induction. Keep reiterating that you do NOT consent to it, and say you are strongly requesting a CS instead. This will back them into a corner if you start to get near the date they want to induce by, but hopefully they will have agreed to do CS before then.
Good luck and keep posting on here, you will get lots of help.
Sorry you are being out through this.