It's very kind of you to be concerned for your friend. The book which ommmward mentions is very reassuring about how children learn. It often is not possible to demonstrate "progress" in a school way but that doesn't mean that the children aren't learning. It isn't necessary to do formal "work" in order to learn well; my children don't do formal work. A good indicator of whether children are likely to be learning well is their overall well-being. If they seem happy then I would bet good money that all is well with their education. If they unhappy then if it's possible to fix that, their education will improve. (I think that is a big part of the reason why removing unhappy children from school sometimes gives dramatic results educationally: when they are happy, they can spend their mental energy learning rather than worrying.)
I think the important question is whether things are good for the family in general. When you say that your friend is struggling, do you mean that she and the rest of the family are unhappy? If you know what is causing the stress, perhaps you can help there.
Experience of many HE families is that the LA home ed department often lacks understanding of home education and does more harm than good. It may be that the involvement of the LA is counterproductive here.
By contrast, I think that Social Services more often gets it right. They seem to show a better understanding of the many ways that families can work well even if they don't match the stereotype of a "normal" family, and to recognise when help is needed. Of course, they can make mistakes like anyone else.
Social Services would not have ongoing involvement with the family if the only concerns were over the education. It is not all that unusual for someone (perhaps even the LA home ed department) to make ill-informed referrals to SS because the referrer doesn't understand home education, but that is generally a one-visit open-and-shut case. If it is true that SS is still making regular visits then they must have concerns over the children's welfare.
I realise I am making a lot of assumptions here. But I would guess that either:
- There is no problem except that your friend needs reassurance that everything is fine, and she needs help from the home ed community to get an ill-informed LA home ed department from interfering. Perhaps she needs a bit of help with her family situation (not education) from SS and other people, or perhaps you've misunderstood and their involvement was a one-off and everything is fine there too.
or 2) Your friend is having a hard time coping with life and bringing up her children and this is affecting their welfare and education. If this is the case, I am sure any help you can offer would be of use. The home ed community is quite strong in many parts of the country and it could be very useful to help her get in touch with them. (I am guessing she is not already in touch with them, or she would know that she doesn't have to make her children do formal work and that statutory national guidelines specifically state that the LA shouldn't be demanding proof of progress in education.)
In either case, I think that a tremendously helpful thing to do would be to encourage her to get in touch with local home educators or if that isn't possible, a national organisation (some of which have good helplines) or a chat board like this. If you want to say what part of the country she lives in, I am sure someone can help to put her in touch with a local group.