I feel like an interloper here, given I only found myself here out of vague curiousty of how other nationalities feel about by country but:
Chances are your contract will allow you to leave after a period all long as you give sufficient notice. You'll need to read it. The last time I rented it said I just need to give a calender month notice.
But, normally you need two things to rent somewhere in the UK, a reference from a previous landlord and a bank account, because they mostly want to take the rent straight out of your account.
So my advise is to stay there for the shortest period you can get away with, leaving on a positive note, and use the time to send up your UK finances (assuming you haven't yet).
That way, you'll find renting again easier.
Also, as long as there's no particular reason you need to in East London, could I suggest trying somewhere in West London? Take a trip on the District Line to Wimbledon. It's lovely and the rent will only be a bit more expensive (about 100-150 a month more).
Oh, and trust me, it gets better. I've been in London for 8 years, it was tough at first but now I can't imagine being anywhere else yet.
Mark.