Brown discharge while pregnant?

I am currently 19 weeks pregnant. Two weeks ago I started bleeding (sudden, bright red blood) at work and went to A&E to get it checked out. They did an internal exam and an ultrasound scan but couldn't find anything wrong with me or the baby. They thought it might be a low-lying placenta, arranged for this to be checked during my 20 week scan next week and advised no sex until then.

The bleeding stopped after a couple of days but I have continued to find a light brown discharge when I wipe (and a small amount in my knickers - sorry for tmi). At first I assumed that it was just the last of the old blood coming out but it has continued at the same rate for two weeks now. I haven't got any other symptoms - no pain, cramps, sickness, etc. - but I'm starting to worry a bit that this isn't normal.

Has anyone experienced this themselves or know what might be going on?