I think it's the wrong question though. Morals have changed (yaay for that) and it's no longer seen as awful to be unmarried (and/or single) with a child.
Agree very much with pp who have said that the right question is why do so many women, married or not, leave themselves [financially] vulnerable after having a child. The Gender Wage Gap is real (hint: it is not necessarily about your hourly rate) and pension poverty for women is even more real. So what women should be doing is educating themselves about how to be as sure as they can that if the worst happens (death, divorce, disability) they are not left financially stranded. (marriage as such is still really a financial transaction).
For all those who say "nah - cohabiting is fine": why do you think gays and lesbians fought so long and so hard to be allowed to marry? We heard a lot in before times about how a dying partner's family came in and sold a house from under a gay partner, took all the assets etc etc.
So of course one way around that is to be legally watertight with everything - wills, insurance policy, clear demarcations of ownership. Also if you do decide to SAHM (totally fine if that is what you want, totally not fine if it's because "i have a big man job that i can't possibly compromise by child sickness, school runs etc" and it is your only option) - make sure you have access to discretionary spending money, claim child benefit to get pension credit, and make sure that you have a life away from home/children. If it is financially possible, your partner's income should pay into a pension for you. etc etc
A marriage licence is 46 quid. I don't know if you have to pay for the registrar's time, but if that is the difference between legal security in case of death/divorce/disability - then it is 46 quid well invested. (and even then it is better to be legally watertight in terms of insurance, property, pensions etc etc. Belt and braces is never a bad idea). If you don't want to marry, or partner doesn't want to marry: "legally watertight" are the watchwords.