I too have this problem. I take spatone (like PPs) every second day with orange juice and every other day take Fab iron. I do still get slightly constipated but have found that when I eat home made museli with yoghurt it helps...not sure why though it just does it for me.
I also ran into my SIL mother today and she said when she was pregnant they recommended parsley as well for low iron, so it can't hurt and my garden is overflowing with parsley so I'm adding it into my diet.
As for the supplements kicking in...I still haven't noticed a great difference. The midwife has had me on Fab iron since 13 weeks as I naturally have low iron but in all honesty I'm still exhausted and dizzy...to be fair though not sure how much is low iron/low bp related and just being hot and bothered and being in the 3rd trimester.