I just wrote quite a bit, giving you 2 ways to move forward, and the website wiped everything out in an instant, and now I don't have time to do it all over again. I won't short-circuit what I wrote, but will come back later tonight. Just ask you a few questions:
1. How old are you and is your BF? In their 20s women are usually about 5 years more mature regarding family and love than men.
2. Which of you are adult children whose parents divorced or were never married? I did my second doctorate research dissertation on the love lives of adult children of divorce. And unmarried childrearing is far more common in UK than in USA. Adult children of divorce or never-married parents are unconsciously afraid of lifetime commitment, so they'll try to believe that what they're doing is something different that will work out better.
It looks to me like trying to avoid the supposed pitfalls of marriage means you're supposedly doing it all YOUR OWN WAY, and therefore learning many things well known in traditional cultural habits THE HARD WAY, by trial and error. So instead of having a ministerial person tell you what being parents and married means, you'll need to consult a couples' therapist to learn what's up for you to learn each time a problem arises.
Also your esGF problem arose at around 3 years together, which is the normal time for romantic passion to subside so you can be raising your child instead of just passionate about each other. But I have to go to the doctor for my poison oak, and then my girlfriend's house for other work and then building our 5month old relationship 1 year after my therapist wife of 31 years died of metastatic cancer. I was her sole caregiver right up to the end--so I know what marriage can demand of a person, and what almost all wives and way fewer husbands will give to that commitment.