I assume you're in London UK? If so, these are the rules:
1. If you conceive using fertility treatment at a licensed clinic, you can elect for your partner to be counted as 2nd parent at the time, then she can go on the birth certificate.
2. If you're civil partners when you conceive, she can go on the birth certificate.
3. If not, you can get make a Parental Responsibility Agreement, which involves all people with Parental Responsibility (which would just be you) sweaing at court an agreement to give another person PR. You would both have to go to court with the firm and swear it in front of someone, then it goes on court record as an official document. You don't need a lawyer, you an just ask the court office for the forms.
4. Because of number 3, adoption isn't necessary. However, some people still choose to go through adoption just so they get a new certificate with both names on. The problem is partner adoption must go through the same procedure as any other so that means social services reports, court hearings etc before it can happen. Also, as partner adoption are seen as lower priority than children in care, it can take a very long time. When I studied 2-3 years ago in our area the average was 2years 7months!