Yup, good answer from Factor - don't recommend going over your direct line manager's head until all other avenues there are exhausted.
It may seem entirely logical to you, but it is your employer you are going to have to convince. With very few exceptions (returning to work after childbirth being one) an employee doesn't have to right to reduce his/her hours.
Not clear why you gave a best answer to alwaysconfude's answer - amybe its what you wanted to hear. That answer is clearly relevant to that poster's company but it has no relevance in law - you and your employer could agree it at one day's notice if push came to shove.
Yes, I'm a former senior HR manager, amongst other things, in my career.