I haven't had this problem while still pregnant, but there's a simple trick you can use while nursing to keep them from leaking - maybe it will work when you're still pregnant too?
When you're nursing, you can usually feel when you "let down" (I have no idea if you can feel this when preg). When you feel it, simply cross your arms across your breasts and put some gentle pressure on your nipples. This stops the leaking. Works like a charm! Of course, if you can't feel it, this won't work since you'll be spending your whole day with your arms across your chest :P