Ah, if you have home educated before then there is a possibility that you could still get benefits. The rule is somewhat vague, saying that you must have home educated before the young person was 16 and not stating specifically that you must have been home educating continuously just before that age.
IMO it could be interpreted in either way. There are home ed advocates who insist that one or other interpretation is clearly the correct one. The paper form asks you when the young person was first educated somewhere other than school or college. It also asks you when they were last at a school or college. But the online form has slightly different wording, which wouldn't enable you to tell them that your child had been HE during primary, so maybe it's better to use the paper one?
I rather doubt that you'd get a correct authoritative answer in advance from DWP which you could rely on them sticking to. So it's hard to work out whether you could afford to home ed. But if you do go with home education anyway, it is definitely worth a try to put in for benefits, fill the form in and see if you can get them, and maybe appeal if they say no. You'd have nothing to lose.
edyourself.org/articles/childbenefit.php
Note that with respect to young people continuing in education, underlying entitlement to Child Benefit qualifies you for Tax Credits. The detailed Child Benefit forms which ask all about the education are the only detailed forms you'll have to do. You'll have to notify Tax Credits separately, but they will follow the Child Benefit decision as to whether your young person is in qualifying education.
The other questions on the Child Benefit follow-up form CHFTE.4 can be tricky, as it isn't written with home education in mind, so take expert advice on filling them in if you aren't sure what to write. It is easier to get it right first time than to be rejected and have to appeal!