Shell, clearly University of Birmingham is not a problem. I just wanted to ensure that you were not thinking of transferring to an unapproved college or school.
Ensure that you apply for an an extension to your Student Visa
before the old one expires. You can make your application within the 28 day period before the old one expires. Apply using
form FLR(S). From that you will note the application fee is £500 in person at a PEO or £250 by post. Don't worry about applying by post and the fact that it will take a bit longer. Even if the application is still pending when the stated expiry date of the old visa is reached, as long as the application was submitted prior to that stated expiry date, the old visa is "treated as continuing" under legislation commonly known as Section 3C. It is treated as continuing until they deal with the application, and if it happens to be rejected, until the time expires for lodging an appeal.
In other words, you would not suddenly become an overstayer if you have not heard the result of your application by the stated expiry date.