Being in a LTR without being married is no different to working in a job without an employment contract. It's fine when things are fine, but once the wheel stars to come off, divorce, illness, death, things turn VERY messy.
The idea of being scared of signing a contract which ultimately protects YOU is perplexing to me.
Let's be serious for a minute. In the UK, marriage is only of benefit to a woman, there is virtually no negative consequences, unlike there would for a man.
As a woman, especially if you have kids together, you WILL get primary custody. You absutely WILL get to stay in the marital home, and HE will be forced to pay for it. You will be entitled to half his pension, half of any assets acquired during the relationship, and there's an extremly high likelihood of you being able to get half of all assets he acquired before he met you. It's an absolute golden ticket, that you'd be an idiot to pass up.
It's nothing to do with the state getting involved in your private life. It's a cast iron guarantee of having access to money and assets which you otherwise wouldn't be able to get your hands on.
You don't even need their agreement to divorce them anymore.
Why any sane adult, with children to provide for, would walk away from that level of protection is beyond me.