noblegiraffe, the non-biological mother can only adopt the child if the father agrees to sign away his parenthood. Otherwise, the non-biological mother can get a PRO (parental responsibility order? not sure) but she cannot legally become a third parent.
It probably seems a lot of semantics, but it can have real consequences. If I was to die tomorrow, my dd2 (adopted) would go straight on having my dp as her legal mother. But dd1 (who has a loving involved father, but whose primary parents are and have always been me and my dp) has no legal relationship to my dp and it would be absolutely down to her father what happened to her.
I think the strongest argument that my dp could use in that situation would be about not splitting up siblings, because of course the law recognises the relationship between the children.
I recognise it's a complicated issue, but I do think it's a shame that the law doesn't recognise the reality that some children DO have three parents. Or even four. We always wanted for our dd to have a father and to have a close and loving relationship with him (and he is a great dad, so I can't regret it) but it is a nonsense that there is no legal recognition for a parent who was there at her conception, at her birth, who has changed her nappies and walked up and down with her through the night and picks her up from school every day. The law recognises as a couple in terms of assessing us for tax, benefits etc. It recognises us as a couple for the purposes of adoption. But it won't recognise us both as parents unless my dd's father agrees to renounce his fatherhood of her (which of course he wouldn't do, and we wouldn't ask).
Sorry, that was a longwinded answer to a simple question!