The Home Office service standard for a standard visa application is 15 working days from the date you supplied their biometrics (normally this is when you attended your visa appointment).

Unfortunately the University has very limited influence over Student visa processing and has no means of expediting student visa applications. 

The latest in-person registration date for your course is 3 weeks after the course start date, hopefully this does allow you a little flexibility with your arrival date.

If you have paid more for a Premium or Super Premium ‘priority’ service for visa processing, the expectation is that the visa would be processed within five working days, but there are some delays with this process during this peak time.  Usually by the time you have raised your delay with the University and the University has received a response from the Home Office (five working day turnaround) your visa is actually processed but if it is outside this timeframe you can contact the Visa and Immigration team who will do their best to assist.