I'm not sure if they give the same leeway nowadays, but I was signing on for a while a couple of years ago, then was offered a couple of hours a week work, which could vary from 2 hours a week to perhaps 35 depending on how busy the company were, I went in and told the officer this, and she said to keep a record of my hours for the first month so they could get an idea of what my average weekly hours were, so they could see how much benefit I would then be due on average. They let me keep the full benefit for that month, as they saw it as a step to me getting permanent fulltime work. As it happened, it did, and quite quickly too.
would your employer be amenable to letting you do perhaps 2/3 full days? at least then you could sign for the other days of the week, instead of having it spread out over the 5 days.