Don't worry, bleeding gums is a temporary side effect of doing Cambridge (or any other VLCD for that matter). Combination of factors (1) you're not producing as much saliva as usual because you're not chewing (2) reduction in the level of Vitamin K in your body (probably don't need to worry about that because your body soon adjusts) (3) you might just be brushing your teeth more often to get rid of the ol' ketosis breath.
It's not a particularly well known side effect but from time to time there have been threads here with people asking if it's normal. It is - and it should clear up by itself in a few days. Doesn't hurt to be extra kind to your mouth for the next few days though - p'raps get yourself some mouthwash to keep everything healthy.