My Rights on a zero hour contract??? HELP??

Hi, Im currently finishing my final year of Engineering Level3. We have had a struggle completing the work with 10 teachers leaving us! I have manged to complete units to my desired level. This week my school has hired back ( for this week only) one of my previous teachers, in a desperate measure to get a unit complete.
I have work to bring home every night this week which so far has taken me to around 10 each night, Which is no big issue, this is my problem...
I work for the Fast Food chain McDonalds, and i was given a shift this week for 16:30-22:15 I advertised this shift to other employees on monday (three days after being given this weeks shifts) this was as soon as i found out this weeks work load.
I rang my boss telling him i will not be able to work whatsoever....
I told him that my school work is more important than work, he understood that.
He began to tell me that he still expects tosee me in (which i can understand). I frequently tried to tell him hat i cant attend, and that i have given him plenty of warning.
Does anyone know what i can do, what my rights are he has threatend me with 'Further action'.

Clue is in the name: 0 hours.

Your manage needs to brush up on his employment law knowledge. Ring them and thank them for the offer of shifts but unfortunately you are already occupied.

A couple of years ago I would have said this but since then I worked on a zero hours contract and in my contract there were extra clauses. It basically said that if I had been 'assigned' work (i.e. given my hours prior to turning up) then I was obligated to honor them and if the workload exceeded those hours I was obligated to complete the work past the hours specified. Now, I personally think that's despicable but I was bound by that contract and I don't know whether those clauses in the contract overruled the 'zero hours' or whether 'zero hours' was the overruling part. But you try to argue that with your manager/employer and it gets incredibly messy.

Also, regardless of all that, I found that on a zero hours contract - when I turned down work they would 'punish' me by simply not providing me with any hours at all for the whole of the subsequent week. They weren't doing anything illegal so that got away with it.

Personally, I'd politely tell them you're not working that shift and see what they say/do and then I'd look for another job because zero hours are exploitative (that's actually exactly what I've done tbh).

Doesn't sound like you were on a 0 hours contract then, as most people would define it.

It was. It was for a company which exclusively offers Zero Hours contracts and who happen to have just collapsed. Unless I'd read the small print in my contract I would never have had a clue about those extra points and as I say, I'm not even convinced as to whether they were legally binding due to the contract being Zero Hours - I'm more convinced that it was scare-mongering by the employer.