Until they are due to be in compulsory education (i.e. the term after they turn five) you can do what you like with them-and supported places in nursery should continue to be funded.
If the nursery is willing then of course your friend can continue beyond that-although there may be both funding, registration and insurance issues which mean their ability to help is less than their personal willingness. Contrary to what has been said, nurseries are not obliged to offer places unless they break discrimination law by not doing so, even if parents are willing to pay. In practice, this means they must offer spaces fairly to under school age children, it doesn't meant they have to provide for children who could otherwise be in school.
The difficulty will be in arguing that nursery is providing a suitable level of education. Although they operate within the EYFS, many do not have a qualified teacher providing planning, and fewer still have teachers actually in the room all the time. Many nurseries feel they are not 'allowed' to teach reading due to the lack of qualifications in those doing the teaching. It would seem to me very hard to make the argument this was suitable or equivalent on its own. Perhaps combined with other schooling but that, like all cases, would be assessed on the individual education on offer.
The other point is that you seem to be writing here of a child who would otherwise be in Reception. Infant Class Size rules will apply until the end of YR2, and so it may be a space doesn't open up in the school until Yr3 or, if it does, there is someone higher on the waiting list (although siblings in school will help significantly). Nursery may be an option for this year, but not for the ones after, and your friend therefore needs to think now about putting plans in place either for home ed or for another school too.
I don't know the practicalities, but wouldn't enrolling at another acceptable school, with appropriate teaching and introduction to school life, be better than staying at nursery for an indefinite period? The cost implications of nursery (both fees and loss of income providing home ed) will impact on the family (and are likely to be significantly higher than the corresponding sacrifices in traveling to a more distant school) the child will need to move settings and friendship groups anyway, and much that is learned about 'school' will still be applicable.