Changing child's surname UK England

I am wanting to change my childs surname from double barrelled (mine first, his last) to just my surname. We are in the UK.

I am currently safeguarding my child and she has had no contact since last year and prior to then it was very minimal due to him being in and out of prison and in addiction and was always supervised by myself. I currently have an ongoing Police investigation against him and I will do everything in my power that she never sees him again. Prior to this investigation, he was never bothered about her, never provided for her, saw her because he thought he had to and im talking like twice a year. Hes worse than scum. My child has never known any of his family and the surname associated with them all is not what I want my child to be associated with. Hes still in active addiction and I dont know where I stand to change her name. Do I need to do a specific order or do I firstly need to apply for contact to be stopped as this is already more or less done now.

I have wanted to do this for a long time but would like to be able to get her a passport without the double barrelled name and just wasnt the association gone.