Am I being underpaid? Is this workplace abuse of overtime?

I’ve had 2 previous roles in hospitality and I never signed a contract at the start, I was just paid by bank transfer and they were minimum wage. I even worked 5 days in unpaid training for one before I got the job. I currently have a part time job at a takeaway where is work 1-4 days a week from 4:30pm-10:00pm. Since I have a full time job as well I get taxed 20% of my pay at the takeaway and get paid £9.60 p/h (I’m 24 years old and the minimum wage is £10.42p/h) except I only get paid from 5-10pm so I take home £48 a shift. I’ve been told to come in at 4:30 to open shop clean the floors and general workspace but I also can’t calculate the end of day totals till it hits 10pm so I normally finish at 10:15pm and even finished at 10:30pm once. Am I being underpaid? Is this workplace abuse of overtime?

Yes, you are being underpaid. Checkout the answer to "I often start early, or leave late, should I be paid for this time?" (on this HM Government web site):

"Additional working time added on to a worker’s shift, before the start or after it ends should be paid at least the National Living Wage or National Minimum Wage. Examples include time spent passing through security checks, attending handover meetings between shifts or helping to open up shop before trading begins.

Think you might be underpaid? Your employer could owe you back pay. Report this to HMRC or call the Acas helpline for confidential advice."

Thank you for your reply! I will try calling Acas tomorrow, do you have any advice for bringing up the topic with my employer?

Well, I'd contact the Acas helpline first, as they may be able to give you guidance as the best way to raise the subject.

Instinct tells me that getting others who work there on your side would be the right thing to do, but they might be happy with the current arrangement and so may inform your workplace before you're ready.