I think you used to have to be married, but very much doubt that is the case these days.
Is this helpful in seeing the difference between adoption and getting PR? raydensolicitors.co.uk/blog/should-my-new-partner-adopt-my-children/
You don't say if any of the biological paternal relatives are involved? Is there any chance bio dad will step up in the future? I don't think they would need to contact bio dad if he doesn't have PR.
I, as an adopter, think adoption is a huge thing. It can be fantastic, giving permanence and security, and being clear who legally is who. However, as mum to a child who has an absent father, I don't think I would go for adoption in his case, no matter how great my new partner. Adoption severs all legal ties will the biological parent, and that is a big thing. In my younger child's case, the legal ties to birth family are certainly best severed to give the best chance for my child, but with profound effects on identity, etc.
I believe, but haven't tried the system, getting PR for extra people who are doing the parenting, is simpler, legally, than adoption. It may avoid opening a can of worms, causing adolescent identity problems, and is less final. It would mean that if you died, your partner would be able to exercise PR just as you have been doing, and cause no disruption, that your partner can consent to medical procedures, and that your partner had to consent to you taking your daughter abroad. But going for PR rather than adoption means your partner is not her legal 'dad'. Since bio dad does not have PR just now, I would research what sharing PR, either by an adoption or a PR order, means. If I didn't share PR for a child, I'm not sure I'd voluntarily give up sole PR. But then I have been in an abusive relationship, so that influences my thinking. Do you want to have to have your partner's permission to take your child abroad, which school, etc etc?