The problem – my wife had an mpg4 but it wouldn’t play on the machine upstair. Needed an AVI instead. I couldn’t be bothered learning all the various settings of ffmpeg (libav is a fork) but found an acceptable (albeit inefficient) way of getting the same quality in the AVI as in the MPG4. OK, the file size was 3-4x larger, so I would recommend optimising things if doing multiple conversions, but this is a good and simple answer for the occasional one-off.
ffmpeg -i original.mp4 -sameq converted_version.avi