Work Experience

Hi guys, my school has asked us to find a place where we can do work experience at the end of our GCSEs. I want to work in technology when I'm older and I have an interest in developing software, engineering and generally science and maths. However, I don't think many companies are willing to let a 16 year old in for only 2 weeks. If you know of any places that you think would be consider my application or even a company that is in that sector I'd really appreciate it. Also preferably in London.