Marriage is great if you are both happy with that as a solution- in which case, I hope a ring appears very soon!
A legal option if yous stay unmarried is a 'cohabiting agreement' which would set out what you each agree would happen if things went wrong in the future. I really recommend getting in touch with Anne McAllister at Morrisons law firm in Wimbledon who is both lovely and knowledgeable. (I was discussing this very matter with her recently.) https://www.morrlaw.com/lawyer/anne-mcallister/
If you don't have a will, please also do this now! At the moment, if one of you died then in theory the assets would pass to the children when they are 18 - not to the surviving spouse. And there may be the 40% inheritance tax to pay, depending on the level of assets. It doesn't need to be complicated to do this - a straightforward 'mirror will' for each of you to leave assets to each other and then pass to children after is what people usually opt for. It would also include who you'd wish as guardians for children which is important if, in the worst case of all, neither of you was around. (If not specified, the local council decides.)
I can assist here or can introduce you to someone locally. There have certainly been recommendations here in the past as well.
Another area that families often think about whilst dealing with this gloomy topic is life assurance while you have dependent children. It's not what you asked about so I won't go into details, but feel free to get in touch. (FYI, I'm a financial planner and wealth manager, and I can tell you from many clients that you are most definitely not alone in what you had previously thought. I'm glad you've brought some light to this subject.)