So you declare MH issues when you applied for the job. Did this mention anxiety, especially social anxiety? If so, did they refer you to Occupational Therapy?
You really need to consider whether the issue is to do with your anxiety, ie, you really don't think you can do it at all as likely to get a panic attack, or is it more that you just don't want a job that involves travel?
Firstly, yes, they can ask you to travel and no it doesn't need to be explicit in your current contract as contracts can be amended and such things added, all legal as long as 'reasonable' and this would likely pass the test of reasonability (assuming they are paying all expenses of course).
Your best course of action is to have a pleasant, non defensive chat with your boss and explain how you didn't expect to have to travel, that it makes you feel very uncomfortable due to your anxieties. You need him to clarify if it's likely to be a one off or very occasional (in which case, maybe you could consider it?), or whether it is indeed part of the job, in which case, you need to ask to be referred to Occ Health. They will then do an assessment and from there, decide whether they take that part out of your job, move you to another job, or decide that as you can't do the job and there is no alternative, they have to let you go.
Frankly, unless your boss shows total sympathy and support, I would start looking for another job as it is likely not to go forward in a way that will satisfy you.