Excellent advise from Blake Barbera, not only does doing as many work placements as humanely possible give you a fantastic oppotunity to work in the field it boosts your CV, an when it comes to writing your dissertation you will have already people to interview, as well as bounce ideas off.
I have found that the best way to gain work experience in the UK, especially london is to email your chosen office direct. I was often advised to write to the offices but an email is quick, and to the point. This shows that you appreciate that they may be busy. If no one responds to your email, and you are a bit brave, call them!
I actually got my current placement by just showing up at the offices! Although I would not say this works often. Any other tips?