No references?

Graduate here...

I have been offered a job based on satisfactory references. Now my problem is my attendance at university was pretty bad because of my mental health. I had a couple of attendance meetings, although I did leave with a 2:1 and my module grades were always between 60 - 70

If I ask my module teachers to give me a reference would they? like they probably don't even know who I am which is understandable. If they did give me a reference would this put off the employer? a graduate with terrible attendance and bad mental health.....

I have asked if they accept character references but honestly so stuck on what to do. I guess if all else fails I will volunteer for 3-6 months to hopefully get a reference that way.

They won't mention your mental health at all. If directly asked about attendance, they are required to answer honestly, but not all employers ask directly. Otherwise, it's generally accepted to be part of the tutor/lecturers role to give references, so just ask.