You have a right to be part of the baby's life, but not of its mother's life. There have been a few cases recently, where the man fathered a child because a lesbian couple wanted a baby, and he did them a favour, saying he wasn't interested in the child, But when he saw the child he changed his mind, went to court, and got access. The court thought only of the benefit to the child of knowing its father.
Assuming the father is you, try to get your name on the birth certificate. If the mother refuses, insist, and go to the registrar of births to make your own declaration. That helps a lot. Get a copy of the birth certificate. Make the child a ward of court if there is the slightest chance of the mother running off and disappearing. Check with the Citizen's Advice Bureau if any of this is not clear.