Marriage is a partnership regulated by the law, even when it breaks down. On divorce, either party would be entitled to claim spousal support and a range of capital provisions such as a lump sum, transfer of any property and a pension share. A court will make the order dividing the assets fairly between the parties with the intention of meeting both parties' reasonable needs and sharing any surplus thereafter, usually 50/50 between them.
If the parties are living together, there is no recognised legal partnership and no cohabitation law to regulate the breakdown. There is therefore no consideration at all of the parties' reasonable needs or fairness. It can leave one party comparatively wealthy and the other homeless without an income.
The only claim a parent with care of the children could make relates to the welfare of the children. Only in very wealthy cases could a parent claim a 'carer's' allowance for themselves.
At that point, they would also be required to leave the house and their own claims would be limited only to that which they are legally entitled and can prove, such as an interest in the family home in civil proceedings. It would be an expensive, uphill struggle, particularly since legal aid is not available.
On death without a will, the intestacy rules provide for all or some of the estate depending on its value, to pass automatically to the surviving spouse free from inheritance tax. Neither occurs on the death of a cohabitee. There are also lifetime tax benefits.
My advice to the 'poorer' or 'dependent' partner, particularly with children, is to strongly consider marriage. It is certainly not a glorified piece of paper and in most cases I have seen in my career, it is a godsend.