One way of finding a work placement or internship is by researching companies yourself and sending a speculative letter and your CV. A speculative letter is one that inquires about the possibility of a company providing a work experience opportunity (rather than applying for an advertised position).
This approach does mean putting some hard work in but people have been known to be successful. Here is some advice on researching:
Focus on small/medium sized companies (SMEs) as most large companies will already have fixed internship and placement programmes
Have a clear idea of what you want to achieve from a work placement/internship
Think about where you could you fit in? What skills do you have to offer? Does your past work experience or the focus of your studies fit with their areas of business?
Try to be specific about the experience you want to gain
Researching Companies: What do you need to know?
If you are planning to send some speculative applications, ensure that you thoroughly research the companies to which you are applying. For more information see: Company Research
Below are some directories for London/UK businesses: