I have been asked to look at this for you.
I cannot deal with immigration/residential status/Brexit issues for you but I can tell you how to deal with parental responsibility for the child.
It is absolutely straightforward and it doesn’t matter whether you are married, not married, or in a civil partnership although you are quite right, it is not possible to have a civil partnership for heterosexual couples. There is a big argument which says that is sex discrimination and that heterosexual couples should be able to have a civil partnership but it depends whether you want to start making new law!
If you both want parental responsibility for the child, then all you do is make sure that the father is also named on the birth certificate as the father. It will be necessary for the father to attend the register office at the time of registration of the birth.
In English law having the father’s name on the birth certificate (or a couple being married) confers responsibility on any children of the couple.
Can I clarify anything else for you?
I am happy to answer any specific points arising from this.
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