i would assume they would be considering the people who are actually employed as a "nanny" or "au pair" as opposed to private baby sitting arrangements. a lot of nannies and au pairs have found themselves forced into registration by smarter parents who know that they can get child care benefit (registered care) payments - it's only 60 odd cents per kidlet per hour, but there are many claims going through - as a result, the carer has to registered with FAO, which ripples to other departments so they can't hide it so much. i do tend to agree 20% is probably a conservative estimate though
I have done both - cash in hand, fully on the books, and been a registered carer. For jobs where parents wanted me to file the paperwork, I charged more. Silly not to, I reckon.

I don't think there's many that do cash jobs long term. Leave isn't so much an issue, but super was what stopped me doing it.