What happens if I go over due?

Hi I had an emergency C-section with my daughter and I'm now 34 weeks pregnant. i saw my consultant yesterday and I've been told I have to go straight into hospital as soon as I show any signs of labour. This I'm fine with but wondered what happens if I go overdue I was 10 days late last time and I was induced but was told yesterday that if you have had a previous c-section they don't induce you. So does anybody know what will happen how long would they let me go overdue before I would have to have another c-section. Obviously hoping this doesn't happen but wondered if anyone knows.

Claire x