Where to live in London with a budget of £750 per month

I will be doing masters in London, likely at Queen Mary (UCL if I get an offer) in Law and Finance. My lectures at QM will be at the Lincoln's Inn campus most of the time.

The following are a must:
Safe location
Commute no longer than 30 mins
Double bed

The following are desirable but I can give up on them if I have to:
No flat share
Plenty of sunlight

What areas can I afford with a budget of £750 per month (£800 at a stretch) with the above criteria?