flowery Of course there has to be consideration that is is due to being part-time. If everyone else is part-time too, it won't go anywhere.
The OP needs a written statement of reason in accordance with the Act as a first step. To simply say bad luck, is wrong, There may well be a way to address the issues.
"6.—(1) If a worker who considers that his employer may have treated him in a manner which infringes a right conferred on him by regulation 5 requests in writing from his employer a written statement giving particulars of the reasons for the treatment, the worker is entitled to be provided with such a statement within twenty-one days of his request.
(2) A written statement under this regulation is admissable as evidence in any proceedings under these Regulations.
(3) If it appears to the tribunal in any proceedings under these Regulations—
(a)that the employer deliberately, and without reasonable excuse, omitted to provide a written statement, or
(b)that the written statement is evasive or equivocal,
it may draw any inference which it considers it just and equitable to draw, including an inference that the employer has infringed the right in question."