I'm 39 (nearly 40) and on my first pregnancy. I have a fibroid about 7cm in size - obv was much smaller before pregnancy, I didn't even know I had it until 12 wk scan when it was 4cm. I have had 1 extra scan at 32 weeks and today am seeing the consultant midwife to confirm whether I can go to the midwife-led unit to give birth (due in 5 weeks) - this is expected to be allowed. I have seen a consultant twice, but she was at pains to stress that otherwise this was a completely straightforward pregnancy, and that they did not want to medicalise it just because of the fibroid.
If the fibroid is blocking the baby's exit route they will discuss caesarian with you, but if like mine it's right at the top of the uterus they will not view this as a necessary precaution.
Even if I have to go to the general hospital, I should still be able to try and labour in their midwife-led unit because in itself a fibroid is not viewed as a high risk element of pregnancy.
Honestly I wouldn't let this worry you. They will probably want to keep an eye on you, but a fibroid isn't really something to worry about. Yes they can cause problems - but if they do monitor you you'll know about these in good time.
good luck xx

Update: saw consultant midwife and she is perfectly happy for me to go to the midwife led birthing centre and not the general hospital. Fibroids are usually not the horror stories you read on the net. Moral of the story: stay away from Google!

i was told i had one when i was pregnant with my now 2 year old i was given no cause for concern and i even forget i have it its only when i went for a scan in this pregnancy that i was reminded when i was asked if i knew i had one (obviously my notes are never read) but once again it was brushed aside so i am not concerned by this