I had a similar problem with my employer. When I first started worked all my shifts, it came to the result that I was underpaid by 22.75 hours. Luckily, however, I had a time sheet which recorded all my hours.
A little later, during my next shift, I told them that I had been underpaid. Later, I bring in my hours sheet and it seemed that the extra hours I worked weren't authorized so I didn't get paid. The manager, after quite some hassle managed to sort it for me and I got my extra hours worth of pay bumped onto my next payslip.
It's a lot of hassle and I know how you feel right now. As they have only payed you £5.30 hour since the beginning, I can't really see your wage increasing unless your pay is stated somewhere on a contract (I assume you don't have salary so probably not)
Those extra hours however should be paid. You have the right to go in. If you have a time sheet I recommend you go in and do what I said. If they still say no, well, perhaps a tribunal could be held (obviously you will not retain your job after this) but you'll get your money. Besides, do you really want to be working anymore shifts for a company that doesn't even pay you for your work? Personally, if it continues I would refuse to work anymore.
EDIT: Tribunal is an extreme measure obviously. There are so many other methods to working this out.