Should maybe have mentioned before that I have a MAX232 in between the sender equipment and my Nano, and I can run the MAX232 at much higher speeds.
Probably irrelevant, so the failure to mention it is understandable.
Found that it I lower the speed from 9600 to 4800 it works perfect, but surely it must be possible to run faster than 4800??
What is sending the data the SoftwareSerial is reading? This is using Arduino 1.0, right? Is that device what you lowered the speed on?