Why did she run away?

The only thing that could explain it and i'm reaching for straws here is that she was scared that he was plastered all over the news and that it might somehow lead back to her or he might turn her in?. Obviously at the time we don't know she has any connection to it. At the start when she takes Owen back to the flat, I thought she had this thing of making homeless people feel so bad that they killed themselves etc. I was totally wrong about that but she was involved in another way. I was surprised at the ending, that Owen didn't react badly to the news that she was involved with the death of an earlier man etc. I didn't expect them to hold hands and jump. Also was the first man's death just random and cos she could do that or was there a link that I missed?. Did she kill the Deacon herself or get him to do it?

She was there but they weren't looking for a woman. It's all about the blinding effect of prejudice. They presumed it was a bloke committing the murders so they were only looking for a bloke. And he was there at both those crime scenes getting off the tube and following behind so they thought they had their culprit and didn't look any further, and he was scruffy and homeless so that was another tick in the guilty box. Once they'd clocked him they were never going to pay any attention to a pretty, petite, well dressed blonde girl, getting off the tube in front of the victims, who didn't look like she could punch her way out of a tissue paper bag. And that was way she needed him in the first place - to be the muscle as the DI said at the end, and as a means of misdirection. In the murder of her former boyfriend, she was in front of him going down that ally way so had obviously got off the tube ahead of him; she knew him, where he lived and had obviously been planning all that happened in advance before finally acting on it, so could quite feasibly have tailed him beforehand to get his journey patterns. People are creatures of habit and don't very often deviate from their normal routine. There would have been a certain amount of chance to the series of events happening as they did, but that's the conceit of TV/Film/Theatre etc. It's a conflagration of possibilities to tell a story and show us something. In this case, don't let preconceptions about people blind you about their capabilities. And also that the unlikeliest of relationships can happen between people you'd never imagine would be together if need/circumstances put them in each others path - despite all you think you know, people will always surprise you.

One thing I don't really understand is how she got him to help in the first murder after they had only known each other a few hours? Is it that Owen had only ever known rejection and isolation and as soon as someone shows him kindness and care he'll do anything to keep it? At that point he didn't know about the baby so what did she tell him about why she wanted to kill the deacon?

I rewatched the episodes about 6 times that week figuring everything out about it - I want to watch it again to pick up on the points that people have raised about certain elements of it but can't. The performances from Jack Roth and Leila Mimmick left me emotionally wrung out every time I watched it - don't know if I could do that again!!