Such a tricky one. It's always a difficulty when one party changes their mind on something as important as this, though of course you are completely entitled to change your mind.
Was not getting married a conscious decision, or something that you sort of drifted in to?
How is the house and the finances and all that split?
There are things you can do to protect yourself and tie yourself together legally - powers of attorney, wills and cohabitation agreements - but they cost a lot more combined than just popping down the registry office.
IMHO, if the reason one party wants to get married is because of legal and financial security then I think they are fine to put their foot down and say it feels essential to them. A SAHP who has little or no income would be very, very foolish to do that without the protection of marriage, and any partner who rejected marriage in that situation would be hugely unfair to do so (and that would be what would make me question their commitment).
However, being blunt, I do think if one party changes their mind on the emotional, 'love' point of marriage then that is different, and the other party is still entirely fair by saying no, they don't want to get married.
But at core it really comes down to the reasons why a marriage didn't take place earlier in a relationship, and the reasons why one or both parties were anti-marriage (and I'm saying that as someone who is consciously unmarried)