""The children were fed by the teachers for some time - the children told us as loved the food one teacher brought in .
It seems it's the school that have suggested the breakfast club rather than mum looking for help . ""
I don't think that what the OP thinks is happening is.
Many do not realise that schools can implement upto a Levrl 2 CAF, or be heavily involved with a full CP plan, it sounds to me that's what is happening. In light of the death of D Pelka, no child is going to be left without family support over the school holidays.
"My friend tries to help the children"
No you don't, otherwise you would be reporting the neglect (if it's happening). Children in families that are very dysfunctional/chaotic learn how to lie and manipulate, it takes very careful questioning to find out what is actually happening.
It sounds as though this family is in the "system", but the OP does come across as being judgmental about this.
It also sounds as though the neighbours are enjoying the curtain twitching, whilst not doing what they can (report, phone the police), to make life better for this woman and her children.