I did my masters on the legal differences between marriage and cohabitation upon breakup. It was a decade ago and things are inevitably going to be marginally different, but the basic law remains, unfortunately, the same. There have been no legislative changes.
There is NO SUCH THING as common law marriage. It's a myth.
If you aren't married, you are treated as two strangers with a shared place of residence. Whoever put the most money in to a property gets that out. If the property is in one name, then it's their house and the other person can have lived there years without any rights if they didn't pay towards the mortgage or provably invest heavily in it - and that's monetary investment, labour is worthless. Childcare and housework are meaningless too.
If you are a SAHM and perform all the domestic service of the child(ren) and home for 15 years and then DP meets someone else and tells you and the kids to get out, then you have to leave. You have no rights. All you are entitled to is statutory child support.
If you marry and become a SAHM, you are seen as an equal party to the marriage, with domestic labour as valuable as his paid employment. If he meets someone else, you have formal legal rights of occupation to the family home, even if it's in his sole name and you've never paid towards it in money. You can even register this right against the property on the Land Register, to alert anyone if he tries to sell it from under you. As primary carer, stability for the kids is a key aim of the courts and if possible they will be kept in the family home - he will be the one to leave, if you're a SAHM or the person with primary childcare responsibility. You will be entitled to a share of all family wealth and assets - which will be put into one pot for division by any court - including house, savings and pension, and while various factors shift what percentage (who looks after the kids as they may need more, how long you've been married as a short marriage obviously means less of a share, as does any "remarkable contribution" by one party) the starting point is 50/50. As a SAHM, you can sometimes get more than 50% if 50% wouldn't adequately house and provide for the kids. And then you are still entitled to that statutory child support, too. But on top. As well as.
I've met women who say they won't get married on feminist grounds, whilst only working part time and doing almost all the childcare. They are bonkers. Marriage is the best legal protection available to anyone who undertakes domestic responsibilities for a family that impact their earning potential. And the hit of a career break is lifelong, in most cases. It doesn't mean you can't still have a good career later, but it does mean you are almost always going to be behind where you could have been, and part-time working almost always leads to a "Mummy track" in high flying careers, too.
Having kids, and planning to stay at home at all? Marry.