Well
assuming that the medical condition you have brings you within the protection of the DDA 1995 then you may well have a case.
Under s.4A if an employee is placed at a disadvantage because of some provision, criteria or practice applied by employer, the employer is under a duty to take such steps, as it is reasonable to take, in all the circumstances to prevent that effect.
s.18B(2) envisages such steps as including … altering working hours.
Thus your request should have been looked at by your employer and allowed. The employer has a potential defence of justification but I doubt he could run this for something simple like a drop in hours in a retail shop.
Remedy for you is a claim to an ET, which must be brought
within three months of the act complained of. Before bringing the ET claim
you must have submitted a grievance and followed the stat grievance procedure to its conclusion.
Draft a grievance letter and hand this to your employer ASAP.
I have attached below a sample start and end to a grievance letter that I drafted for a friend last year.
I am writing to tell you that I wish to raise a grievance.
This action is being considered with regard to the following circumstances:
DETAIL, DETAIL, DETAIL – Times, dates, locations, names, copies of any written requests etc I am entitled to a hearing to discuss this matter. I am entitled, if I wish, to be accompanied by another work colleague or my trade union representative. Please reply within (not more than 2
8 days of the date of this letter.