Yes this is a good idea, as said fhey don’t need to confirm in writing or give a written justification, but you can put what was said in writing and email it to them.
the union can’t do much here, you need to follow process.
explain your disability and how it comes under the ea.
explain the impact it has on your ability to do your job.
explain the reasonable adjustments required and the impact on your performance
explain why you feel these are reasonable, as in they will not disrupt the business, they won’t impact other staff, you will be able to do your job as per someone without a disability, and why it’s proportionate and why it’s affordable.
the latter they should do, but as they are declining it’s good for you to rebut
no one here can say it’s discrimination, as we don’t know the above details. A business can reject a request if they feel it is not affordable, proportionate, or is disruptive and impacts other employees. So it’s hard to say these are reasonable, and they should do it, this discrimination or no not reasonable
as said though, the union can’t do anything more than support and advise, the singular body who can decide is an employment tribunal.
so raise your grievance, give the above detail, and then they need to follow that process.