I realise now the Airport list is showing available networks in the area, but there is one dominant one that my computer keeps flipping to and then disconnecting. It has come back into the Preferred Networks box mentioned above. Can I block that particular one somehow?
It shouldn't attempt to connect to anything that you yourself haven't previously tried connecting to. I believe you said you've already done this, but the procedure to remove an unwanted (previously connected to) WiFi connection is to go to:
1. Apple Menu => System Preferences
2. Network
3. Select AirPort (or Wi-Fi if you have 10.7) from the left window pane
4. Click 'Advanced' button in the right window pane
5. Select the AirPort (or "Wi-Fi") tab. This should show any previously connected-to network. Select the network and click "-" to remove it.
6. Click OK
7. Click Apply
8. Close the window.
If this truly is what you've already done, I would also recommend changing your wireless router's "channel" setting to something else as the offending network may just be sending out a more "palatable" signal (although it really shouldn't be trying to connect to it without your say-so). Also, be sure you're using WPA security (not WEP) and have SSID broadcast ENABLED.