how long from head engaging to labour?

[nixpix]

This is probably a 'how long is a piece of string question' but if anyone has any similar experiences to share, I'd be grateful. My baby's head has just turned down from being breech at 36-37 weeks. I had a scan yesterday to confirm this and am now 37+5. The head
was 'free' at the scan yesterday. When should it start engaging and how long does it take to get fully engaged? Is there a rough time scale between being fully engaged and labour starting? This is my first birth.
I have polyhydramnios and fundal height currently 46cm, so keen not to go over due date by too much! Irony is the hospital kept emphasising how I might go into pre-term labour and it looks like it will probably go the other way.
Thanks.

It is a 'how long is a piece of string' question.

Head was engaged at 35 weeks, dd was born at 39+6.

Ds never engaged and was born at 39 weeks. Would love there to be some definite answer on this as have been engaged on and off for weeks.

The baby can become engaged as early as 33w and still go to full term, I don't believe that the baby becoming engaged actually determines the start of labour as there are lots of things that affect the rate at which the baby becomes engaged, such as:

Well toned stomach muscles
Being sporty
Having a larger baby
Sitting down for a long time
Pelvis shape/size
Already having had a baby

Def a 'piece of string' question. DS was engaged at 37 weeks. He was born at 42 + 3!

DCs 1 and 2 engaged fully at 32 weeks (v uncomfortable),

DC1 was on time, DC2 a week early

DC3 engaged during labour - he was 10 days late

Their strings were obviously different lengths

Many thanks for all your replies. Am hoping my piece of string is shorter rather than longer...
Will let the thread know actually what happened.

Oh yes, do let us know! Good luck

About twelve weeks for me.

Well, a little update. I'm pretty sure that I lost my mucus plug this morning, or at least some of it. Rather like a load of pork pie jelly (as someone else described, but is exactly like that. So hoping we're going in the right direction. I'm sure though that I've not had any BHs yet in this pregnancy. A few period type pains that come and go but no 'tightenings'.
Fingers crossed this means something will happen before my due date - 2 weeks time.

my dd's head was engaged at 36 weeks and i was 12 days late.