I had epidural when I gave birth to my first baby. It was good and I did not have any problems with it afterward (now my baby is 2.5 yrs). It worked on me quite well and I did have topped up once . (from getting epidural to baby came out was about 4 hours)
I gave birth in Auckland City Hospital and no appointment required but just asked for it whenever you think you need. How far you can get it done depends on how busy the theater is by the time. Mine was got just a few minutes after I asked for.
You can discuss it with you MW and Auckland City Hospital provides with the introduction and you can book for it and talk to the team.