There are very few "accidents" just people taking stupid risks. Maintain a safe distance, ie enough manouvering room so you don't join an accident, don't overtake when you can't see the end of the manouvere e.g going up hill or on a bend. Stop when necessary. Procede with caution sometimes you might want to turn off the radio open a window and listen. Use your indicators. Drive within your lights or as conditions allow. Don't be an asshole.
Sometimes you will come across assholes on the road it is best to give them a wide birth even stop and pull over in order to get them out of your way, but don't dawdle if you want or need to drive slow make opportunities for people to overtake.
Bad planning and poor judgement are the most common causes of accidents which is why schools have low speed limits around them as kids can be stupid around roads.
Be helpful, I remember one time I was filtering down the centre line on a motorbike (dispatch rider) past stationary traffic and a taxi driver stuck his hand out. I braked and a pushchair popped out from between the stationary traffic. Without that warning I could have killed a toddler as it was no harm was done and I don't think the mother was ever aware of the danger.
One thing about london traffic professional drivers work the streets most of the day and they are very road aware. The most dangerous times are when schools start and when schools let out, followed by the rush hours when the non professionals are on the road.