I'm sure this uncertainty isn't helping your depression at all. Your union can give you advice and will not take action without your specifically requesting them to. For completely anonymous and reliable advice try
http://www.acas.org.uk/
, they are excellent and there is a telephone helpline too. Two things you may want to know; your employer has no reason to consider your medical condition unless you have declared it to be an issue. However, being unfit to do the work can leave you open to dismissal. The person with a small child who is not being moved has to have his or her needs considered in the light of the latest "family friendly" part of the Human Rights Act, and this is not preferential treatment, just different.
Talk to ACAS as the distance you are being asked to move may be regarded as unreasonable if it's far enough.
If you have to move, try and see it as a chance to make new friends (other people will probably be as worried as you are about this) and learn to cope with change. I do hope it goes well for you.