Also, we have nothing to leave bar a few grand at the moment. We would sort out wills when we had something to leave (ie the house) but until then its barely anything.
You should still make a will. What about your children, do they not deserve to be considered if you died? Wills aren't just about money. If you both died in a car crash tomorrow, who would raise your kids?
As it stands now, if your DP died tomorrow, the couple of grand he has in the bank would go towards paying for the funeral. Anything left over would have to cover any debts he has, and anything left after that would go to your children - you'd have no access to any of it. You'd also have no say over what happened to the money left for your DC.
And blaming not being taught this in school is a bit naive, really. You have enough knowledge to get online and post this, so you could quite easily have gone to google and done your research.
You're very vulnerable, but too many women (because it's pretty much never men who leave themselves in this kind position), don't realise how vulnerable they are until it all goes wrong.
Are you at least named in each other's pensions? If he does a dangerous job, does he have "death in service" benefits? If so, is your name down to receive those? If not, again, they'll pass straight to his NoK which are his children. You won't get a penny.
It's the people who have nothing who are most protected by marriage. Widows' benefits are another thing you'd be entitled to on his death if you got married. Currently in the eyes of the law, you are a single parent and won't get a penny in support. Can you afford to lose out on that £120 a week if he dies?
Can you afford to raise the DC alone without all the support of wills, pensions and marriage?