Breach of contract?

[Realistic1234]

I currently have a part-time job as a community support worker. When I started I agreed verbally to 20 hours per week gave my availability as 7am-7pm, 1 late a week and every other weekend (which was also written But not in the contract).

Over the last few weeks a few issues have arisen.
Being Rota'd on for over 6 hrs without rest break.
Changing my Rota several times since collected, which I didn't mind until I wasn't informed of cancellations by the office, my Rota was changed the night before I started, and in 3 cases my Rota was changed and I was not informed at all meaning I turned up at the wrong service user/time and had to cancel medical and dental appointments.
Not to mention the constant harassment by phone, text and email to do extra hours or contact the office to the point where I don't answer the phone if they ring unless they leave a voicemail saying it's urgent.
It came to a head when I collected my Rota on the day before the next working week began to find full time hrs, which I informed I could not do. In addition several times I was put to work 11 hrs between 7.30am and 10pm and then start the next day at 7am. When I mentioned I understood that there should be 11 hrs between work days I was told community support workers were an exception to the rule and they could only cancel the first appointments making me start at 8am.

I am ready to leave. My main question is do I have cause to walk away or will it be me breaching contract as by now it says I must give 1 month notice. I am not interested in resolving the matter as emails back and forth to admin have not been productive and I have a second job I can focus on.

Thanks for any advice.

[TrippingTheVelvet]

You can look and see if you're on zero hours. Personally, I would tell them you're not doing more than twenty hours but I wouldn't walk out the week before Christmas. It will mean the other care workers which are mainly mums and young students will have to either work more over the festive period or vulnerable people will go without care.

[Realistic1234]

My contract doesn't mention how many hours of work, so it may well be zero hours. That was agreed on verbally at interview. In regards to telling them, I have multiple times, only to come in to a Rota with 35 hrs on it with the rest break issues i have mentioned. Their response to everything since I have started has been we are short staffed despite employing over 100 people. My impression is that it is more likely poor organisation. I am not uncaring but I don't want to be taken for a fool and made to feel awkward every time I insist on basic working rights, regardless of what time of year it is.