Has your manager said why they won't implement these? Are you in a union? Have you contacted ACAS?
If you work in a customer facing role, I think it would be seen as unreasonable in the same instance as that if you accepted a job in a call centre, but then requested to not work on the phone.
You would be requesting a change to your overall responsibilities and role within the business.
It may be that your employer has employed you to do this job, and the workload you have cannot be shared out between existing staff.
Equally, shift pattern wise, it will likely be down to scheduling and whether or not your request meets the demands of the business. For example if there are already people with flexible working patterns in the business which means that as they require so many people on shift on certain days, they cannot accomodate your request, in which case it would be seen as unreasonable.
However, you should be invited to a formal meeting process, where they discuss the request and the outcome of the request as well as give you the opportunity to appeal the decision. If this has not been done you may be able to take them to an employment tribunal, usually within 3 months less 1 day from the original date where the instance occurred, such as your request for reasonable adjustments.
It is up to the business to provide you with reasons for rejecting your request as well as providing evidence to back up those reasons.
If you are disabled the business is obligated to make adjustments however these must be reasonable and what is reasonable is different for all businesses, big and small.
I think what would be seen as a reasonable adjustment in your instance would be to allow you to spread your breaks throughout the day so you have more opportunities to step away from work during your shift, and to allow you reasonable time off to attend appointments which may benefit you. It would also be reasonable for them to provide you with some sort of counselling as many places provide EAP services.
If you are not in a trade union I recommend joining one, however many won't assist with pre existing issues, they may still offer advice.
I also recommend giving acas a call, so they can provide you resources for representing yourself both formally and informally.