There's a thing called the Bystander Effect (I think it was that - it's a long time since I did my degree!) - essentially if there are lots of people that see something like this happening, they are more likely to assume that somebody else will phone the emergency services/step in to help/etc - partly British reserve, partly people not wanting to get involved or be the first one in a group to make a move as they're worried that they might be wrong or stepping on somebody else's toes or whatever. And the more people there are around, the less likely anyone is to do anything to help.
There are a couple of ways around this.
Once you know about the effect it means that you know that nobody else will step up - so be big and brave and step up and do it yourself. If you need others to help you, rather than just asking 'the crowd' for help, ask specific people for help - they find it harder to say no when asked personally. You might find somebody says no, I'm on my way to pick up the kids from school and late, or I don't know how to do that - but they will often help if they don't have a reason not to. Even better, ask people to do specific things - please could you (person in a coat) ring the ambulance, please could you (person in a blue coat) help me put them in the recovery position, could you (person in a black coat) look out for the ambulance to flag it down and bring them over here, could you three over there just help to keep everybody else clear and give this person some space.
Alternatively if you are that person that is injured and needs help and there are lots of people around, target somebody and specifically ask them for help if you are able to, even if just to get them to call the ambulance/etc - one specific task, especially if you need emergency services, is often enough to reassure a person that you're not about to attack them or ask them to do anything too onerous and most people have a phone on them to ring the emergency services - and once they are talking to the emergency services, they will kick in and ask about the situation and ask them to do more things if necessary, rather than you needing to.
Many times - in the uk at any rate - the people that do stop to help without thinking about it are those that work in emergency environments or those in which there are critical things going on and so they know about just stepping up and doing it. On the other hand, apparently in the US it used to be that doctors would actively not step up because if anything went wrong (even if not their fault or because they did the best with the knowledge they had but it wasn't enough) they could be sued... not sure if that's still the case but they need to be really careful.