Thanks SurferTim - changing the LED pin to 9 fixed it. You have kick-started my confidence!
The circuit diagram I have, which I thought was for the Arduino Ethernet is obviously not the right one, because it shows the LED as being on pin 13. The diagram is titled ARDUINO ETH Rev 8d.
At the moment there does seem to be a shortage of information specific to the Arduino board with integrated Ethernet, as opposed to the Ethernet shield.
Many thanks again