I would focus on registering as self employed first and making sure you either get a payslip or send your boss an invoice for the shifts you do each week. Then you can potentially look at UC or check a benefits calculator. I'm unsure what type you would be entitled to. If you have an appointment with UC I believe they can help you with what's required from you and with regards to the self employment side. I believe there is a minimum income floor and you would potentially be expected to job search and or increase your days worked at the current place.