My 14 year old step daughter wants me to adopt her. She wants nothing to do with her real mum . Does my step daughter have the right to get this done without her real mums permission

Not until she is 18.

You MUST have BOTH biological parents' permissions in order for an adoption to happen, or a court order by a judge that deems a parent unfit--which is harder to do than you'd think.

What is the situation here? Is the father (your husband I assume), the custodial parent or is the mother? Does she spend time with the mother now? If the father is the custodial parent, does the mother pay child support?

As a minor, the step daughter has NO right whatsover to get this done, whether with or without the bio parent's approval. An adoption has to be initiated by an adult. So you would have to file for adoption and part of that process would be getting the bio parent's approval.