What are my rights? Can I leave my job?

• social work
• work injury lawyer

Ok, so 4 weeks ago I wrote a letter to my work asking for a change in hours due my a change in my husbands work meaning I don't have the same childcare. The day after I handed it in my boss came to me and said it will be no problem to change shifts (it's only changing the day I work) as there were other shifts available. I said that was great and I had a few weeks so would happily help out until the

end of the month. This week I asked my boss what date they had planned for my hours to change, she said I would have to wait until they recruited someone else for my shift as they were already short staffed that night. The reason they are shirt staffed is because another member of staff was disciplined and now moved to another department, this only happened last Friday! This however should not be my problem. I can not continue to work this shift passed this weekend as a I previously told my boss! I have not revived anything in writing as a response to my request to change my days of work so can I just leave! I'm pretty sure I need to give 4 weeks notice but as they have not responded to my letter can I reduce the notice to one week! I actually have no childcare for next weeks shift.

Additional Details

I should probably add that I only work 9 hours a week and am quite lucky that I don't have to work, my primary job is taking care of my kids. Had my boss told me I would be unable to change my hours at the time when I first handed in the letter I would have had to resign then. My problem is they have only just told me I can't change and have left me with no choice but to leave without the correct notice.

What are my rights? Can I leave my job?