Hello and thanks for your question.
With or without your girlfriend's consent,you cannot be registered as the child's father if you are not the child's biological father. That would be fraudulent - and is probably a criminal offence.
You want to bring the child up as your own. In other words, you want parental responsibility for the child.
Mothers automatically have parental responsibility (PR) for their child. Fathers acquire PR a) by marrying the mother of their own child b) by being named as the natural biological father on the child's birth certificate c) if they MARRY the mother of a child who is not theirs AND the natural father who ALSO has PR agrees, they can all three signed a parental responsibilty agreement.
None of these apply to you. An adoption order does grant PR but is only used for children in the care system - so that also does not apply to you.
When you have been living with the mother and the child for three years, you can apply for a child arrangements order or a parental responsibility order. A child arrangements order can specify with whom a child is to live and with whom a child is to have contact. When a biological father applies for this order, the order automatically confers PR - but the court would consider the situation much more carefully if someone who was not the biological father applied.
Alternatively, you could apply for a parental responsibility order. Again, this is an order that is usually applied for by the biological father, so the court would consider the situation much more carefully if someone who was not the biological father applied.
The natural biological father would have to be given notice of any court proceedings including adoption that involved his own child, as he has the right to have his views heard by the court.
I know this was not the answer you were hoping for, but it would be wrong of me not to be honest with you and not to give you the correct legal position as I see it.
You may like to have some face-to-face legal advice from a specialist family law solicitor.Here's where to find one:
I hope this helps anyway, and I wish you the best of luck.
Thanks and best wishes...