In the UK you could refuse to consent, although this would leave the options of waiting to see what happens or a CS.
Talk your options through with your partner or someone who can support you; be clear with them if there's something you know you don't want, even if you're less clear about what you do want (after all, you haven't been given other options yet). Then call the hospital back to discuss the plan with your support person included. Your supporter needs to be able to tell the midwife or doctor to stop or let you have a discussion or time to think if you need a minute.
It helps if you can look up risk factors first; the RCOG website is useful for this, e.g., CS can halve the risk of stillbirth but increases risk of maternal death, etc. Look at the risks around induction for your age group. 1:10 fail - what's their plan for that? What was your Bishop score when they examined you? Under 5 and an induction is much less likely to be successful.
When you've checked out the risks and options, you can decide what's right for you and push for that. For example, you could suggest a plan where, next week, if your Bishop score is below 5, you won't have the induction but will go straight to CS (if that's what you want - the point is that you have options for discussion).
I know this is daunting. I did refuse consent to induction - over 100 hours into a failed one. It was 4am, I hadn't slept in over 24 hours and the head of midwives was sent in to try and talk me around. I refused to change my mind so they sent in the consultant at 9am. He was also unsuccessful and had no good argument as to why the induction process should continue any longer (he offered to have a rummage with his 'magic hands' - I declined as politely as I could manage, which wasn't very). By midday DC1 was safely delivered by a lovely CS (I'd been induced originally because of gestational hypertension).
Unfortunately it is horribly normal to be treated as though you have no say - I suspect this is why the education women receive about childbirth is so woeful, it's less effort for staff.
Best of luck 