Deposit to afford to move home

I currently live in a property in a bad condition. My landlady is a family member so I don't want to gain extra priority on the re-housing list by getting her into trouble. I am a single mother of two young children and I am struggling to save for a deposit to move to another property as they need deposit, month up front and admin fees.  I work full time and my wages are not bad at all. I do however pay £150 per week for their childminder as the hours I work don't allow me to take them to school. I don't recieve any benefits and this is my last resort. I desperately need to move house for my children's health and my own. I just don't have any extra cash after I budget. It is really hard for me to ask for help, but I don't know what else to do. sorry for the sob story, but thank you for taking the time to read this Coleen x