When can you request voluntary redundancy?

I currently work in a back office role in a large company. Our department is closing down and we have been ‘mapped’ to new roles which are in a Call Centre. Call Centre work is my worst nightmare due to anxiety issues. However we have basically been told, if you don’t like it you can find a new job. Unfortunately, for me I work part time and have 2 young kids so finding a new job is not proving to be very easy. I have been with the company for 13 years and have always been in back office roles. They are also asking me to come in for four days a week for one month for training which is a nightmare for childcare. Can I request voluntary redundancy if the new role is not suitable? A handful of people have been given it for medical conditions i.e. ear problems, but I don’t know if having bad anxiety will be seen as a valid reason.