London there are two methods of induction - one involved a pessary or gel on the cervix which releases hormones and tries to encourage the body to go into labour naturally. I didn't have this as my waters broke first and then contractions started naturally, but I think it's relatively non-invasive and if it does induce labour then labour can often go on as normal.
If that doesn't work, then they give you syntocinon via a drip - it's a synthetic version of oxytocin (I think, trying to remember from last time). It makes the uterus contract which progresses labour, but the contractions are often much more intense than with natural labour, so most women on the drip end up with an epidural to manage the pain. It also means your labour will be much more medicalised, as you'll be monitored more closely. There's also a chance it won't work and you end up needing a c-section anyway, although I can't remember know the percentage of women that affects so don't know how much of a risk it is.
I had the drip as my labour didn't progress, but because DS was at an awkward angle, he basically got stuck and therefore was squeezed and distressed by the contractions. I ended up with a c-section, but induction or no induction, I would have had one anyway as he was in such a weird position that I doubt he'd have ever come out vaginally. It was a one-off due to his position and I think it's highly unlikely to happen again, so I'm not blaming the induction for me needing a section. The reason I'm refusing is because it wasn't a pleasant experience being induced because DS was stuck and distressed and his heartbeat kept slowing, which meant on several occasions the midwife had to press the emergency button and a flood of doctors came running into the room, concerned about the baby until eventually his heart rate came back up, only for it to happen again every time they tried to turn the drip up. It was traumatic, and I don't want to bring back memories of that if I get induced so I'd rather have a repeat section.