Here because I need the same advice. Sending love.
If you’re not married then in the UK you don’t have to put his name on the birth certificate. They would then have to apply for a parental responsibility order from the court in order to try and get on it and to get parental responsibility - from your side there’s nothing you can do until that happens but in the meantime if there’s any abuse/other reasons why you wouldn’t want them having contact then the best thing to do would be to keep record of it all! Hope this helps x
We went through this last year with a step child, feel free to private message me x