On the subject of safety in RP, I notice now that I cycle with a kid, that there isn't a single safe way to get to or from Regent's park by bike. It's true for walking to a lesser extent. The result is that people drive to the park.
I can't help but think that the best way to make using Regent's park safer for everyone would be to work on this. Safe routes to/from the park could cut the number of vehicles in the park, making a trip to RP safer all round.
When I'm in the park with the kid either on foot or bike, it's cars and motor vehicles that cause me the most concern for her safety.