This very much depends on the stage in the application cycle and if your department decides to interview. Not all applicants are interviewed. For undergraduates, you should expect to receive a decision within four weeks, or at the very least notification to attend an UCAS visit day. If you have not heard by the end of this period, please contact the department directly.
For postgraduate applications, the application process is considerably hindered if you do not supply a complete application to the Admissions Office. Please do not send your application to the department. Your application should include a fully completed application form, two academic references, and an academic transcript.
Some departments also request samples of written / practical work. For all PhD applications, you should include a detailed research proposal to enable the department to identify an appropriate supervisor. A complete application should enable the department to make a decision within four weeks. If you have not heard by the end of this time, please contact the department directly.