They are difficult to fine it's true. I looked on Gumtree and
Ebay but fixed wheel bikes were either non existent or were over priced rubbish.
I ended up buying a frame off biggsy, from here, and putting it together myself. I'm not sure exactly what it set me back but it was certainly more than £100.
Have a look at some single speed sites like this one. You might just get lucky.
http://www.lfgss.com/