She must first apply for child tax credits. If entitled to this she can then apply for the sure start mat grant (one off payment).
I understand her situation and sadly perhaps the best option for her is to say that her partner does not support her and apply for income support as this benefit opens the flood gates for all others. I appreciate that she may not want to do this but I can assure you that are a very many who do, and work the system to their advantage.
Cant remember who it was on here but they advised that you should apply for everything regardless of whether you think you are entitled or not. I have telephone the benefits call centre many times and once in a while get some additional info that was not given to me before and have benefited from this. Unfortunately it appears (to me) that there is not one person who is prepared to 'walk' you through the system and look at the options based on your personal circumstances.
I wish you friend good luck.