Working while waiting for HSMP result: In UK as student now

Simple question:

I am a student who has completed his MBA course, but not received the results or degree as yet. I applied for the HSMP visa in July and realize that I will not get a decision till November. My student visa expires in December.

I know that I am allowed to stay in the UK till I get a decision, even if its after the time my visa expires. BUT can I pursue full-time or part-time work during this time.

Many thanks in advance,
Zip