I have the same problem and did so even before I fell pregnant. My levels were very close to anemic when I was tested so my GP put me on prescription iron tablets since the beginning of the year and they haven't really made much of a difference. She thinks my body just does not absorb iron efficiently, but she thinks the baby should be getting enough and will be OK (i'm due in 3 weeks).
I have read that taking iron tablets with Vitamin C does help the body to absorb the iron. So try taking them with a glass of orange juice.
I'm also a vegetarian so I can't get iron from red meat, but their are alternatives like pumpkin seeds, beans, including kidney, lima, navy, black, pinto, soy beans, and lentils, greens, including collard greens, kale, mustard greens, spinach, and turnip greens, tofu, vegetables, including broccoli, swiss chard, asparagus, parsley, watercress, brussel sprouts, chicken and turkey