Hello, I am from the southwest UK, and speaking on behalf of my partner who has had a child with his ex partner. He has come to this decision by himself, and was not influenced by me. I am gaining information for him because he is at work.
Basically, he was with his ex partner for just over a year, 9 months of this she spent pregnant. She got pregnant very soon into their relationship, and she was only 17. She hated living with her parents and kept begging him for a child. He refused because they were young, living in a tiny flat, and had a low income. She stopped taking her pill, but remained to remove it from the packet to make him assume that she was protected. Only when he found out she stopped taking the pill it was too late and she was pregnant. She refused abortion.
Slightly before becoming pregnant, he was going to end the relationship due to mass amounts of physical violence from her (his body is still damaged today) but he stuck out the relationship for the welfare of the child. As soon as she gave birth, she forced him to move out, contacted the CSA and shortly after got a new boyfriend. Now my partner is left paying for a child he didn't even want, put effort into a horrible abusive relationship for nothing, and doesn't even get any access to the child. She has got a restraining order on both of us for no reason at all.
She publicly came up to him a few days ago, and was laughing in his face showing him her new phone which she said 'his money paid for it' she also sarcastically thanked him for getting her pregnant because now she has a council flat and more money than she needs apparently.
I think this is disgusting, and find it shocking that if this was the other way round, the female has 100% control, can have abortion or put the child up for adoption whenever she wants. If a man forced a woman to get pregnant, that is against her human civil rights. So why can she get away it?
I would like to know, if at all how he can sign over the parental rights, and then get the step-parent (her new partner) to adopt the child. Who could he contact to do this, or where could he go?

As much as I sympathize with your partner (and I do) it isn't going to happen. He cannot force someone to adopt, nor is it likely the courts will allow him to give up his rights.

What he CAN do is fight for his rights as a father. Fight for visitation. He can try suing her for deception if he can prove she lied about taking her pills. Bottom line he needs to consult a solicitor to see what rights he has and how to enforce them.

But he has to remember that it was his choice to have sex with her. Her pleading for a baby should have raised red flags for him. But he ignored those red flags and continued to have sex with her. He's going to have live with the consequences of that decision.

This (http://www.adoption.org.uk/information/step_adoption.html) site is a good resource for questions about UK step-parent adoption, which interestingly enough, does not require a step-parent. What you seem to be asking is if he can force the adoption and the answer is no. There is no way to force parental responsibilities on another person because the parent no longer wants them. Unless her partner wants to adopt and they petition to do so, he is out of luck. If he actually wants to step in and be a father to his child, can petition the court for visitation, with court supervision if necessary to keep the peace.

Just an aside... he is not a victim here. He made a choice of who to have sex with, and even used perfectly, no birth control is 100% effective. He certainly wasn't forced to get her pregnant, he had a relationship and ongoing unprotected sex with his partner, with a child as the result.