You're saving money - no tax and no N.I. contributions. At fulltime min wage you earn around 700 quid a month. 8409 a year. 2000 taxable, at 400 quid a year. Probably over fifty for N.I. again depending on your pay. Near 500 a year. At FT you'd get around 1152 more a year, 24 a week. I wouldn't worry about it - it is a cafe it really doesn't matter whether they do it 'properly' or not in terms of how you are affected so just leave if you don't like it. You aren't the one who gets in trouble if they do get caught (which they won't because the government understands it needs to work like this). What they are not going to do is change their business practice and increase their costs for your benefit.
Everyone does this - cafes, pubs, most of the building trade. The reality is doing these things legally costs so much money nowadays that it is better for the business to take this small risk. The government rapes small businesses especially for every penny they can get - because they can't complain and they're still taxing 'the rich'. Also those kind of businesses to an extent rely upon students & young people, itinerant workers etc to function properly. Those people need the flexibility just as much as the business does.
EDIT: Didn't think about the 4.83 figure so I'm gonna change the numbers now. Sorry 36 hours awake here lol. The new figures show you making more money every year. Hope the editing hasn't made that all a nightmare - essentially the first lot was complete crap.