Unfortunately I have to agree with canyou and jessy that this is how it is to be a chef in a small restaurant. My brother has been a very good, highly thought of chef for about 15 years and is beyond totally knackered in his early 30s. He's walked in and out of dozens of jobs in that time, all over the country, mostly in 5 star hotels and Michelin starred restaurants or gastro pubs.
Almost impossible to lead a 'settled' life as moving around all the time. Has been unemployed and back at parents for past year or so due to back and knee problems preventing him working - chefs are on their feet for 16-18 hours a day.
Long hours, ridiculously low pay (definitely below NMW when counting actual hours worked, terrible working conditions). Alcoholism is rife too. I'd say it is almost impossible to find a decent employer wrt hours, pay, working conditions etc.
chains are not much better -DPs cousin worked in the kitchen for a chain and she didn't know barely from one day to the next what her hours would be - she could work tens of days in a row, double shifts sometimes if someone else was off or they were short staffed etc. didn't get statutory holiday entitlement either.
I suppose they get away with it because a lot of the workers are young and either don't know their rights or don't have the confidence to stand up for them. After all, if someone loses their job, there are others queuing up to take it.
Totally incompatible with family life and committed relationships too - chefs are effectively married to the job, not their spouse.
It's not right but unless there's some widescale enforcement, I can't see anything changing and your DS needs to consider whether this is what he really wants or choose something different.