Noticeably, the policewoman kept a fair distance away while talking to the guy and didn't move forward until he'd given her permission to do so. Her general demeanour was calm and respectful and you could see the positive effect this had almost immediately.

Unlike me and her colleague who did, more or less, the exact opposite.

This is very important. I have had the most success when the other person feels in control at all times. Think approaching a wild horse, not saving a baby from a burning building.

Unfortunately, it is also counter to intuition for many, who just want to help and tend to swarm around the problem.

Don't think about approaching. There's nothing you can do if you're next to them that you can't do at a distance. In particular, you should never try to physically stop someone jumping (who is already on an edge). Given that, you may as well keep your distance anyway. The most important thing is to listen.

Sometimes being able to talk in a normal conversational tone is preferable to screaming over a distance.

Maybe he disliked you so much that it made the female officer seem that much better. In the end, he didn't jump. Sounds like you got a win to me.

Can you describe your emotional state?

Do you think it differed at all to the paramedics and policewoman?

Yes, panic. As opposed to calmly dealing with an everyday situation.

The policewoman did have the advantage of being able to close the bridge to traffic though, which also helped calm things down.

There's a reason many country's police forces get trained for deescalation. It's not a natural or easy thing to do for most people