Your new partner can but her natural father can contest it whether or not he is on the birth certificate.
Depending on the age of your daughter her feelings would be taken into account.
This link may be useful
http://www.direct.gov.uk/en/Parents/Adoptionfo steringandchildrenincare/AdoptionAndFostering/ DG_10021340
I was thinking about my new partner adopting my eldest daughter, things aren't working out so well now and I'm really glad I didn't. Don't want to preech or be pesimistic but it's worth thinking about what would happen if things didn't work out with your new partner.
Hope all works out ok x