Advice please

Bottom line is if he wants involvement ideally you need to allow it unless theres safeguarding concerns. If he isnt fussed then leave him be as you cant force him to be involved i fought for my daughter dad to be properly involved since she was born and he has only just started really bothering and she almost 7.
My sons dad isnt on his birth certificate and he didnt bother to get the form filled for me to take as he couldnt come with me due to him being abusive.

He hasn’t been bothered for nearly 24 weeks now he trying to say the baby’s not his and said he moving away and he has blocked me and my family so we can’t even give him any updates about my appointment

I wouldn’t put him on birth certificate, I worked in passport office for a while and had to tell mums all the time if dads on birth certificate we need dads consent to future passports, so if dad isn’t contactable or he wants to withhold consent, your child won’t have a passport until their 16 and parental consent from both parents isn’t needed. It’s not worth the risk honestly!

don’t

Absolutely do not put him on the birth certificate. Absolutely not. It automatically gives him parenting rights. I’d speak to citizens advice!!