Pearson Vue do allow you to change the date of your UKCAT to suit you - within reason (i.e. if you contact them early enough). In fact they advise that:
If you are not feeling well, reschedule your test to a later date – even if this means losing the test fee. In presenting yourself for testing, you are declaring yourself fit to take the test. We will not consider health issues as extenuating circumstances.
Use this opportunity to reschedule wisely. Some of you may feel anxious and put the test further back. Accept that you will have to take the test eventually. If you keep changing dates without a genuine reason, then you run the risk of taking it on a day that is even more inconvenient.