I'm afraid I disagree with Ineedacleaner and Whatatip.
I think there are questions that you should be asking yourself and more importantly your consultant if he/she thinks that you should be induced.
First of all, why is there a need to induce a twin pregnancy before term (and 40 weeks IS full term for a twin pregnancy) making your babies early, especially if you and the babies are healthy?
Secondly ask your consultant to provide medical evidence to back up their reason to induce (and not just anecdotal either).
My twins were born at 40+3 and my Consultant's registrar was really keen to induce me. DP and I were not keen as induction is a major intervention that dictates the rest of your labour and delivery!
Just for your information there is NO medical evidence to support induction in a twin pregnancy that goes slightly over due (i.e. less than 42 weeks) where both the mother and babies are healthy.
I think you were right first time, maybe you just cook babies a little longer. (40 weeks is only an average figure after all and doesn't take your personal ovulation cycle length into account).
Your babies will come when they come.
Medics are there to 'manage' labour and delivery. Multiple births often need to be managed and sometimes the medics forget that sometimes multiple births don't!
Incidentally, I delivered two healthy babies (7lbs 1oz and 7lbs) naturally, the first needed a little ventouse help, the second (breech) was delivered naturally with no help and we were/are all healthy.
Trust your body!
and don't forget BRAN to get the information you need to decide whether to accept an intervention.
Benefits (of the intervention)
Risks (of the intervention)
Alternatives (to the intervention)
Nothing (what happens if we do nothing and wait a bit longer)
Hope all goes well and I'm looking forward to hearing who you had and your birth story!