You must inform your Tutor as soon as possible about any circumstances that affected your performance and s/he will be able to advise you on what happens next. The University Applications Committee has produced this information about the processes which take place when a candidate has experienced extenuating circumstances. Your Tutor will keep you updated on the status of any application made on your behalf.
CUSU has a good summary of the possible outcomes of an application to the Applications Committee and also has a useful set of FAQ for the examination allowances procedure, which includes information on when you should expect to hear from the Applications Committee and what sort of evidence is usually required.
You may also find it helpful to speak to the Chaplain or the University’s Counselling Service about any mitigating circumstances, such as bereavement, especially if the pressure of examinations has not given you time to grieve.