You're probably correct Satin but the OP does say Do we agree there is one, who are they, why does it exist and what can we do? and it would appear if I understand correctly that this term has been recently invented by a think tank, and no we don't all agree on the definition or that it is a totally seperate matter and unconnected to the failures in education for many.
You need to look at why people can't and wont access it, and if one of the reasons is they know lots of people who worked really hard to access it and feel failed by it and can't see the point of trying, then that's relevent but if you insist no they're this outside society's norms unconnected to other people on the margins or in society then all you do is divide and rule everyone involved.
I have asked for more information on the education underclass having an agreed definition, and unlike the term underclass it doesn't seem to be an agreed term, just one that's being pushed by a particular group of people and is there to try and further divide imo.
Our local nursery that was trying to do the things you're talking about, and has done for nearly two decades, has lost its funding again because Ofstead said it was inadequate, again.
It’s not very popular because it serves a hard area including some hard parents and kids, and often parents are refered there as part of trying not losing their kids, the rest are poorer parents who can't travel, and immigrant parents who don't know, so it always struggles to break even and is normally run at a loss.
It always has problems getting good enough staff and volunteers, and it always has problems maintaining standards because of that. It’s a vicious circle that gets ignored.
It’s opened and closed down an awful lot over the last 17 years, it always ends up closed down as not good enough and safety problems and the reasons behind why it deteriorated again are always the same.
Each time it closes most of the kids from it don’t go somewhere else, they go nowhere, because the better nurseries don’t accept the situations of the majority of parents who use it, so it becomes pointless.
The message everyone gets is anywhere that accepts them, isn’t any good anyway.