Question about being induced?

I had a membrane sweep last monday at 40 weeks and 1 day but It hasn't seemed to have worked as I have had no twinges whatsoever! Apparently the baby is totally ready and a nice healthy size (over 7lb), head fully engaged and my cervix is ripe and thinned out and Im 3cm dilated. I have the feeling it won't happen naturally because surely it would have happened by now with me being ready etc (baby's head has been engaged for weeks now) I have been told by the midwife that If I haven't given birth by next monday then she will arrange for me to be induced. (I will be 40 + 8 days then) What Im wandering is, will I be sent to hospital that day or will they make an appointment for like a week later? I feel like Im going to burst!