So based on the last census, there has been a significant drop in the rate of marriage in this country; those that are getting married are waiting till later in life.
There hasn't been an equivalent drop in the birth rate and the rate of very young mothers having children without a partner (i.e those in their teens) has remained relatively flat. These are typically the group of lone parents who are invariably brought into play in these discussions; despite the fact that they make up the smallest grouping of those claiming LPA.
So adults aren't marrying, but they are still having children, LPA costs are increasing year on year and it's not all the teenagers.
Here's my theory - partly based on the above and partly from my anecdotal evidence.
Young couples are having children, ostensibly living apart, and then getting married to each other some years later.
Why would they do this?
Because the LPA pays better than doing it the other way around.
If you (as a couple) believe it is better (or more financially viable) for one parent to care full-time for the children, particularly for the early years; then you can opt not to marry for several years, live apart (or at least have separate addresses) and have one partner claim LPA.
I've seen this phenomenon enough times over the last decade or so to believe that this is the true reason behind the rate of increase of claims for LPA.