Ultimatums never work
They may not work in the sense of getting you what you want, but they do have a way of at least letting you know where you stand.
No-one can "force" this guy to marry the OP, or anyone. This is about the OP trying to find out what the real situation is and where she stands.
Occasionally, you do hear of guys who put off marriage because they can't separate it from the idea of a wedding, and the thought of planning a wedding has them freaked out. These guys are quite happy to make the commitment as soon as this is clarified, and if they know that there is the option of a registry office wedding now and perhaps a wedding later on, even in several years time, or perhaps never. No problem.
However:
When a guy makes vague comments about not believing in marriage or whatever, 90% of the time it means "I'm not really that into you, and am keeping my options open in case something tastier comes along."
A LOT of these relationships break up a few years down the line. Actually, most of them.
When this happens, the woman is often left a lot worse off as a result.
She may have had children and put her career on the back burner in order to take on most of the domestic duties and childcare, in effect impoverishing herself to further her boyfriend's career, and ending up with next to no savings, assets or pension when the relationship ends (there is NO SUCH THING as a "common law spouse" in British law).
Alternatively, she may delay and delay childrearing, only to find that by the time the relationship ends, it is now too late to think about having children with someone else.
The guy, meanwhile, typically comes out of the situation quite nicely off, having forged ahead with his career while girlfriend-pretending-to-be-a-wife has spent the last 5 or 10 years washing his socks and managing the home front. Typically, within a year or so (despite having spent the past several years whining on about how marriage is an outdated institution or he can't get married because his parents got divorced and he is suffering from childhood trauma etc. etc.) he will be married, to someone elseoften someone a lot younger than the previous girlfriendand have kids with her. As we all know, men's fertility doesn't clock off in their early 40s like ours generally does.
OP, I am very far from being the kind of person who yells LEAVE THE BASTARD at the slightest provocation, and I have to say that your situation sounds like a disaster waiting to happen.