I've just had the exact same problem and managed to fix. The first thing to note is that, unlike the old ball cocks, the float valve doesn't stop the flow instantly. It takes a few seconds for the diaphragm to work . Gently lift the float lever and hold for a good few seconds, if this stops the flow then all you need to do is adjust the float.
In my case this didn't work so I took apart the float valve and gave the diaphragm a clean. On reassembly I noticed that the diaphragm wasn't sealing on top of the small conical part. I discovered this by wetting conical part and testing to see if it left a wet ring on the diaphragm; it didn't. I put this down to degrading of the diaphragm so have ordered a new one.
However I couldn't turn the house water supply back on until re-assembled and I didn't want to have to take it all apart again in a few days. So I filed 1mm off the flange of the conical part and that allowed it to sit higher and seal with my old diaphragm.
Diaphragms are only a few pound so I recommend you order one before pulling the guts out of the cistern.
Richard H
Richard H, February 2008
