It's certaibly an interesting metric @icouldbevioletsky but a few things mean the eventual decrease in private participation is likely to be less significant than that 21%:
1.Did they count the CAF responses for previous years as they stood end June or the September total? Some parents might not yet have given up their state place but still will
2.Has the total number of applicants applying to state as a backup really changed in line with birthrate changes, or did increased certainty this year mean that more of the children who will eventually go private applied for a state place than would have in previous years?
3.Is the change in birthrate the same in both private and state sectors, or more pronounced in one or the other? (This could actually shift the percentage either way)
4.The children who didn't apply to state as a safety net in previous years seem like a 'safe' group who definitely won't change to state. So a given percentage of those-who-applied-to-state changing to go private becomes a lower percentage change in the whole private sector year group (although I agree with SheilaFentiman that most probably do)
5.You said that 3.3 is the average over previous years, but how much does it vary?
It's a big increase though! We'll find out more in September.