If you’re looking to do a Masters you can apply for a Postgraduate Master’s Loan from the Government to help towards course fees and living costs. This loan is income-based and you receive payments in three instalments per year. Check if you’re eligible right here.
If you go on to study a postgraduate doctoral course like a PhD, you can apply for a Postgraduate Dount you get is not based on your family’s income. But your qualification does depend on other factors, like your course, your age and your nationality or residency status.