The midwives may have given you perfectly accurate info, but that particular consultant's preference is contrary to the midwives' preference. Which is exactly what happened to me.
DC3 was due and I was 40y. Previous babies had been SVD, at 40w and 41w, in hospital, both larger than average. DC3 predicted to be large. This time I wanted a home water birth. Full support from every member of the midwifery team. Consultant would not sign me off for HB. Told me at 37w - and I kid you not, it's bloody engraved on my brain - "Your baby is very big. You will have shoulder dystocia if you give birth at home. Do you want to put your baby at risk?"
I complained to the senior midwife, who spoke to the consultant, who then signed me off for HB.
Then the consultant began pressuring me to book in for induction at 40w. More scare-stories. Midwives' attitudes were different: yes, there's increased risk after 40w, but you don't need to decide until 40w.
I was scanned at 40w, a fairly in-depth scan, checking various blood-flows, to help me make my decision. I decided to ask for a sweep at 41w+1d, but did not say so (afraid of more pressure to advance it).
DC3 born SVD in the pool at 41w. Astonished everyone by weighing 5kg. Did not astonish me by being the fastest and easiest of my births.
Later, talking with other mums, it seems that those who had had pre-planned CS for medical reasons loved her. She specialised in complex pregnancies, so perhaps saw more danger than midwives, who see ordinary pregnancies and births day-in day-out.