I had twins which was my 3rd pregnancy and was induced at 38 wks with a plan for vaginal birth as lowest twin was in a good position. My personal preference is against epidural and I had coped well with gas and air in first two labours so that was the plan.
I took two pessaries to get going, then it suddenly kicked in very fast and incredibly intense and painful. From nothing but mildest niggling pain, to waters breaking and both twins born was 1.5 hrs.
I was taken to a room next to an op theatre to deliver, with a double team including anaesthetist and doctor in case the need for a section arose as things developed.
Epidural was available as we had a chat about it when things got going as I did question trying to cope with the level of intensity and pain if labour was long, though in the end it was too quick even if I had wanted.
I imagine it varies a little from hospital to hospital, but this was standard where I was in Suffolk at the time.
Plan A was always a vaginal birth if all factors allowed it and that was what both hospital and myself were aiming for, but!!, to be prepared for an emergency or change of plan if it arose. There was no suggestion of planning a section just because it was twins, it always depended on whether things looked good/possible for a vaginal birth.
Contractions went off a little for second baby and they started to murmur about possible section if we got to the cut off time, but things got going again and I could really feel to push him and was very aware of this if that makes sense, so I feel with an epidural it may very likely have been an assisted birth and I was very glad I didn't have one. The doctor did have to help deliver him as he came out arm first, but arrived safely after some shoving it back in manipulation.
It's different for everyone. I had a very good experience. A friend of mine had twins a few years later and her experience was almost identical, so it's possible to have a good, safe induced vaginal birth with twins without epidural.
Though epidurals are not my choice, I definitely don't think it's right not to have the option available and I've never heard of this in a main hospital so you strongly question it and press for it. Going without is not for everyone as induction does make labour intense.
I would definitely discuss it with both consultant and senior midwife, talk about your worries, ask direct questions to try to get some reassurance and answers.