Failed apprenticeship?

I started a 'Business & Administration' apprenticeship at the beginning of December. Since then I was taught basically nothing other than how to use a photocopier and putting pieces of paper in files. I spent most of the day browsing the internet being bored out of my mind because they had no work to give me.

It is a small business and they really had no idea what having an apprentice entailed, I think they were just looking for cheap labour to be honest (£3.00/hour, 30 hours/week). They admitted it is their fault that it hasn't worked out. My last day was yesterday and they said they were going to contact the learning provider to tell them it hasn't worked out, and that the learning provider would contact me shortly after (they haven't yet).

The problem I now have is they said it would be better if I resigned than if they fire me (I know the law makes it difficult to get rid of apprentices). But I worry that if I resign it will make it harder for me to go back on national insurance credits when applying at the job centre (I'm not eligible for JSA). Will they not see it as "he voluntarily chose to leave a job"?

I don't know what to do next, I don't want anything to do with Business & Administration now.