The important question here is 'how long has the toilet been in'. If fitted and problem was immediately apparent, the chances are that the push-button rods have been cut too long, probably only by a millimetre or two. However, if the push-button uses the cable type release and is recently fitted the most likely reason for constant overflow is indeed that the float valve has been set incorrectly. This is easily corrected by simply turning the threaded rod attached to the float. The 'syphon' itself can't really go wrong unless you have snapped something off.
The toilet has been in for about 7 years (the previous owner of my house had it fitted). I think the fault is with the rubber washer onthe bottom of the float valve... it doesn't look too bad but it's the only thing that it can be. Any ideas where I can get parts for Lecico float valves??