Young Couple Trying to Move - Advice?

I'm 21 years old, and my partner and I are trying to move out of our home town (I'm starting a Masters degree in a university in Brighton and we both want to move out of our town because it's awful and expensive). We live in a basement 2 bedroom flat that we pay £400 a month for (incl. Rent, council tax etc.). My partner's father rents it out to us, that's why we got it so cheap, however, he is not renewing the mortgage, and it will run out later this year, hence why we need to move. I'm finding it so difficult to find somewhere affordable for us to live. I'm going to be a full-time student and will be on unpaid work placement all week as well as going to lectures and doing my work, so I have no time for a job. My partner earns over £1,000 a month, and it's hard for us to afford to live even now. As I'll be a postgraduate student, I can't get student finance. Can anyone give me any sort of advice? Maybe how I can get around the money situation? Also, if possible, a list of outgoings when you live in your own place? (We just give my partner's dad the money at the beginning of the month and we don't know the exact cost of everything as he helps us out as well).

Ps. My family lives too far away for me to live with them, and my partner's family have no room for us.

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