I take it you work in retail or something? This used to happen to me and my colleagues ALL the time when we were in retail. To put it bluntly, they don't care. They don't care whether you have other commitments. They know that they can quite easily replace you with someone else looking for a job with those hours. You have to explain to them that you cannot continue working those hours and you complied with their 1 month notice policy, however as far as I'm aware, they do not have to cut your hours/contract if it isn't right for them. You may very well have to leave that job and find another one. Now might be a good time to start looking.