Esspee
If you have a civil partnership or marry then your assets become one. This changes the situation if there is a death or divorce.
All you have told us regarding your financial situation is that you own the house. Suppose you marry or enter into a civil partnership. If you die first and he gets the house then remarries your children will not inherit. It doesn't matter what he agrees to in a will, it can be changed at any time.
If you remain unmarried what's his is his to do with as he pleases, you decide what happens to your assets.
The other side of the coin is that if you do not enter into a civil partnership or marry, your partner can be kicked out of the house the minute you die, by your children who are your legal heirs.
He has no legal right to stay in the house, and may have legally to prove that the things he says are his are bought and paid for by him. I doubt he has receipts for everything he owns,
I don't know about the UK, but here he would not even be entitled to decide, where, when or how you were to be buried or cremated. I personally know of two men who were not even invited to their long-time lover's funeral, and one who was turned away by the family when he turned up.
I suggest you and he talk things through, then seek legal advice on the pros and cons.
Neither you nor he probably have the authority to tell a doctor that further treatment of your dying partner is not wanted. Your children decide that for you by law and I have no idea who his nearest blood relation is, but whoever it is and however remote decides on his behalf.
For both your sakes, sort this out now.