Having investigated further, I have found the "legitimate" solution.
Open the AVG user interface.
Just uncheck all the boxes.
If you go along this route, the AVG icon in the system tray will always show an error/alert condition, so you will need to check that this is not because you are unprotected for some reason.
EDIT: The product recommended by C:\Saw looks good. As he says it isn't an AV but looks to be a good complement to one. In particular it will run on anything from Windows 3.11 upwards, so it must be light on resource.