This is the guidance on the ox.ac.uk website:
Illness on the day of the test
If a candidate is ill on the day of the test but decides to sit the test anyway, they may apply for special consideration. If a candidate does not take the test at all due to illness, the decision about whether or not to shortlist the candidate will be taken by the college considering their application. In the case of BMAT, candidates who fail to take the test are not considered further, unless there are very strong mitigating circumstances.