Hi Marcio,
I'm also new to TSR - what a great forum!!
Although I have to declare that I'm not a student (i have searched to see if it was allowed for "non-students" to be posting but I couldn't find anything - happy to be corrected though..)
In my very first start up we stumbled upon using interns and have never looked back since.
We even took on summer interns from a few US-based universities whose students were in London on a Summer School programme, a part of which was getting experience working for a London-based SME to give them a local flavour.
It was a complete WIN-WIN for everyone.
They got the experience they wanted. Worked on some pretty amazing projects and added lots of value to our company and they had something serious to show for on their CV e.g. "saved the company £££..." / "helped open new markets.." / "increased turnover by..."
As an employer/entrepreneur, this is the sort of achievements I/we are looking for, so if you do get a chance to work with an SME, definitely grab it.
ps. there are agencies out there that offer this service of placing students e.g. enternships
pps. make sure you don't get only the crappy admin jobs (which of course you will have to do, but make sure that this is the smaller part of the time you spend with them)
ppps. for short term rentals there are a lot of short term shared accommodation available in london (I used to be involved with one of them), just search online
Good luck!