From what you've told us here, I would focus on persuading them that you don't want to go out partying, fool around or get secretly married. You only want to focus on your studies, and then explain how they would be negatively impacted in that living situation. Essentially, assuage their concerns, then promote the positives.
Also, you do realize you can take out a maintenance loan if you have status as a home student, which you said you do. This is for up to £8,700 a year, or £11,000 in London and is explicitly for living expenses, i.e rent and food. With that money, plus your savings, plus a part job, you should be able to survive.
Please do correct me if I'm mistaken, but I'm fairly sure that whatever your nationality, if you've lived in the UK for 3+ years and have settled immigration status, you are a home student, and get the same financial support as UK/EU students.