The real answer is that it's up to the ECO. If you have a good reason to be in the UK before your course starts, you can REQUEST a date more than 2 wks beforehand. Going for a little over 3 wks myself, I actually sent them an e-mail. Here are the 2 replies:
"The two week period that you are inquiring about is a general rule that entry clearance officers go by. If you have a special case that you think might warrant more than two weeks, you should make this clear in your entry clearance application, or if you are applying in person, make this known to the entry clearance officer. However, it is up to the discretion of the officer as to whether or not your request will be granted." (British Council)
"You may enter up to a month before your studies begin.
When you send in your application please enclose a cover letter stating your plans." (Chicago consulate)
I've heard of people getting quite a bit of time before their course starts - to visit family, to travel, all different reasons. They evaluate everything on a case-by-case basis. However, since you're NOT entering the UK primarily to work, it's very risky asking for much time beforehand in order to solely work - seems like something they would frown upon. The two weeks (I asked for 3+) are meant to give you time to find housing and a job, not to build up savings before school starts - that's your responsibility before you ever go over.
