Inches short of a disaster

Hi,
This morning a terrible thing happened to me. I was going to a friend's to take her mum to the airport, with my 4 yr old on board. At around 10:45 I was standing at the traffic light facing the Polish embassy to the EU/ING bank, right next to the Jules César tram stop, intending on turning left (no other options there). A car squeezed in on my right, a very unwise thing to do but I had to take it into account as it had right priority over me in case of a problem, so I decided to clear as much space for it as possible as the light turned green. My car was quite a bit taller than that other car and I couldn't see it very well. I was so preoccupied with my intention to turn the shortest possible that I didn't pay attention to the people crossing over at the green pedestrian light by the tram stop. A man with two small children (one in pushchair) was in the middle of it right then, and I managed not to hit them but only just. My car stopped inches from them. I was in shock, and so was the man (probably a Briton). He started screaming and through himself on my bonnet, bashing it with his hands. I couldn't move or breathe or even blink, I was like in outer space. When finally they were safe on the pavement, I pulled off like in a cloud of thick fog. I only had to go another 50 metres or so to the apartment block so I somehow made it and sat there for another 10? 15? minutes, totally unable to move.
I am aware of the kind of comments I am likely to get but my intention here is to present my deepest apologies to this man to whom I didn't say anything, I didn't even make a sign or a wave. I am a careful driver and a mother (and a pedestrian too), and I understand all too well what he went through at that instant and what he probably feels now after it all happened. I just wanted to say I AM SORRY!!!