Do I need to return home to apply?

I have a bit of a confusing situation, but I'm hoping someone can help me out.

I'm currently studying in the UK on student entry clearance. I already have a Bachelor's degree from a US university. I have a job offer here in the UK, and they want to sponsor me. However, my studies will not be 'complete' by the time I start work (all assignments will be finished but I will not yet have my grades and award) so I will be applying for sponsorship using my US-based Bachelors degree (if I remember correctly from the points calculator, Bachelors and Masters award the same points anyway)

My question is - do I have to return to the states to apply? Or can I remain here when I submit my application?

Thanks so much for any help!!!